Below is a fairly brief description of Devi and the multiple emanations/goddesses thereof. Included also is a mantra associated with the goddess. Careful further research into each devi should be undertaken before approaching any of them or using their mantras.
Gāyatrī is considered the veda mata, the mother of all Vedas and an emanation of the all-pervading Parabrahman. the ultimate unchanging reality that lies behind all phenomena. Gayatri Veda Mata is seen by many Hindus to be not just a Goddess, but a portrayal of Brahman himself, in the feminine form. Essentially, the Goddess is seen to combine all the phenomenal attributes of Brahman, includingPast, Present and Future as well as the three realms of existence.[ Goddess Gāyatrī is also worshipped as the Hindu Tridevi combined as one. In Hinduism, there is only one creation who can withstand the brilliance of Aditya and that is Gāyatrī. Some also consider her to be the mother of all Gods and the culmination of Lakshmi, Parvati and Saraswati.
Taat Savitur Vaarenyam
bhaargo devaasya dheemahi
dhee-yo yo nah prachodaayaat
DURGA (Chandi, Amba)
A/The Supreme Form of Devi manifested as a warrioress, destroying hordes of asuras (demons) and removing obstacles to our progression. Her first appearance was in the Devi Mahatmyam, whereby she stepped from transcendant to imminent from the prana of various gods, therefore She is the shakti of all gods.
Om Hrim Dum Durgayei Namah
Mahakali (Chamunda, Badrakali)
A/The Supreme form of Devi within the Kalikula tradition of Tantra. Kali is a fiercer form of Maa Durga, and emanated from Her in the Mahatmyam and other paranic battles. "She who takes away the darkness", Kali is often identified with kala (time), as time catches up with everyone, and therefore Kali is destroyer, the shakti of Shiva. She is a very protective mother of Her devotees and uses Her sword to "cut off our heads", which is to say, render death to our Ego, bringing us to liberation.
Om Krim Kalyei Namah
A/The Supreme form of Devi. Lakshmi is the giver of boons and riches (both material and immaterial), and tends to guild Her children as a loving and considerate mother. Also protective and a bestower of knowledge (the greatest wealth), Lakshmi is the shakti of Lord Vishnu, and grants fertility, thus also is She a sustainer of life upon Earth.
Om shrim lakshmayai namah
A/The Supreme form of Devi that embodies the collective knowledge of the entire Universe. Saraswati is a great muse among the songwriters and poets and is the Devi that forms the body of the Vedas. Shakti of Brahma, she also serves as a role in the creation of things-- both material and immaterial.
Om Sam Saraswatayai Namah
Nine forms of Durga worshipped throughout Navatri, a nine-night festival in honor of Mahadevi and Her victory in the Mahatmyam. Each of the nine are additionally emanations of Tridevi. The first three are emanations of Kali, the second of Lakshmi and the third set are Saraswati. The first three are The below descriptions are sourced from hinduism.about.com
Shailaputri: Shailaputri literally means the daughter (putri) of the mountains (shaila). Variously known as Sati Bhavani, Parvati or Hemavati, the daughter of Hemavana - the king of the Himalayas, she is the first among Navadurgas. Her worship takes place on the first day of Navaratri – the nine divine nights. The embodiment of the power of Brahma, Vishnu and Shiva, she rides a bull and carries a trident and a lotus in her two hands. Om hrim shailaputriya namah
Bharmacharini: She is worshipped on the second day of Navaratriand is the second form of Mother Goddess. Bharmacharini means one who practices devout austerity. She enlightens us in the magnificent embodiment of Durga with great powers and divine grace. She holds a rosary in her right hand and a water utensil in her left hand. She is blissful and endows happiness, peace, prosperity and grace upon all devotees who worship her. Filled with bliss and happiness, she is the way to emancipation - Moksha. Om hrim bharmachariniya namah
Chandraghanta: The third facet of Goddess Durga is ‘Chandraghanta’, who is worshipped on the third day of Navaratri, for peace, tranquility and prosperity in life. She has a ‘chandra’ or half moon in her forehead in the shape of a ‘ghanta’ or bell. That is why she is called ‘Chandraghanta’. She is charming, has a golden bright complexion and rides a lion. She has ten hands, three eyes and holds weapons in her hands. She is the apostle of bravery and possesses great strength to fight in the battle against demons. Om hrim chandraghantayai namah
Kushmanda: Kushmanda is the fourth form of the mother goddess and is worshipped on the fourth day of Navaratri. The meaning of the name ‘Ku-shm-anda’ is as follows: ‘Ku’ = a little; ‘ushma’ = ‘warmth’; ‘anda’ = ‘the cosmic egg’. So she is considered the creator of the universe. The universe was no more than a void full of darkness, until her light spreads in all directions like rays from the sun. Often she is depicted as having eight or ten hands. She holds weapons, glitter, rosary, etc., in her hands, and she rides a lion. Om hrim kushmandayai namah
Skandamata: The fifth aspect of the Mother Durga is known as ‘Skanda Mata’ - the mother of Skanda or Lord Kartikeya, who was chosen by gods as their commander in chief in the war against the demons. She is worshipped on the fifth day of Navaratri. She is accompanied by the Lord Skanda in his infant form. Skanda Mata has four arms and three eyes, holds the infant Skanda in her right upper arm and a lotus in her right hand which is slightly raised upwards. The left arm is in pose to grant boons with grace and in left lower hand which is raised also holds a lotus. She has a bright complexion and often depicted as seated on a lotus. Om hrim skandamatayai namah
Katyayani: The sixth form of Mother Durga is known as ‘Katyayani’, who is worshipped on the six day of Navaratri. The legend behind her name goes thus: Once upon a time, there was a great sage called Kata, who had a son named Katya. Kata was very famous and renowned in the lineage of saints. He underwent long austerities and penance in order to receive the grace of the Mother Goddess. He wished to have a daughter in the form of a goddess. According to his wish and desire the Mother Goddess granted his request. Katyayani was born to Kata as an avatar of Durga. Om hrim katyayaniyai namah
Kaalratri: This is the seventh form of Mother Durga and is worshipped on the seventh day of Navaratri. She has a dark complexion, disheveled hair and a fearlessness posture. A necklace flashing lightning adorns her neck. She has three eyes that shine bright and terrible flames emanate from her breath. Her vehicle is the donkey. Her raised right hand always seems to grant boons to all worshippers and all her right lower hand is in the pose of allaying fears. Her left upper hand holds a thorn-like weapon, made of iron and there is a dragger in the lower left hand. She is black like Goddess Kali and holds a sparkling sword in her right hand battle all evil. Her gesture of protection assures us of freedom from fear and troubles. So she is also known as ‘Shubhamkari’ – one who does good. Om hrim kaalratriyai namah
Maha Gauri: She is worshipped on the eighth day of Navaratri. Her power is unfailing and instantly fruitful. As a result of her worship, all sins of past, present and future get washed away and devotees get purified in all aspects of life. Maha Gauri is intelligent, peaceful and calm. Due to her long austerities in the deep forests of the Himalayas, she developed a dark complexion. When Lord Shiva cleaned her with the water of the Ganges, her body regained its beauty and she came to be known as Maha Gauri, which mean extremely white. She wears white clothes, has four arms, and rides on a bull. Her right hand is in the pose of allaying fear and her right lower hand holds a trident. The left upper hand holds a ‘damaru’ (a small rattle drum) and the lower one is in the pose of granting boons to her devotees. Om hrim mahagauriyai namah
Siddhidatri: Siddhidatri is the ninth form of Goddess. She is worshipped on the ninth day of Navaratri. Siddhidatri has supernatural healing powers. She has four arms and she is always in a blissful happy enchanting pose. She rides on the lion as her vehicle. She blesses all Gods, saints, yogis, tantrics and all devotees as a manifestation of the Mother Goddess. In ‘Devi Bhagvata Purana’ it is mentioned that Lord Shiva worshipped her and was blessed with all Siddhis (supernatural powers). By her blessings his half body became female and other half body male in the avatar of Ardhnarishvara. Om hrim siddhidatriyai namah
The ten tantric goddesses, emanations of Devi which is to the Srividya/Srikulas, She is Tripurasundari, and to the Kalikula tantrics, the honor is given to Kali as Supreme. Caution should be taken when working or appropriating any of the mahavidya, even the gentler goddesses. Some of the information below was sourced from astrojyoti.com and wikipedia.
Kali: The ultimate form of Brahman within Kalikula, "Devourer of Time", see Her Tridevi description for more. Her mantra among the Mahavidya, and one among the most Supreme of Mantra:
Kreem Kreem Kreem Hum Hum Hreem Hreem Dakshine Kaalika
Kreem Kreem Kreem Hum Hum Hreem Hreem Swaha
Tara: Sometimes known as Neel Saraswati, Tara is a devi of compassion whose features are almost indistinguisable from Kali, for in reality there is no difference. She is the defender of wisdom and while render obstructions to acquiring it obselete.
Om Hreem Streem Hum Phat
Lalita-Tripurasundari (Shodashi) Supreme Goddess to the Srividya, a High manifestation of Goddess Parvathi, Lalita is "She who plays" and is "beautiful among all three worlds". She grants boons of wisdom and grace, wealth and love to her devotees. She is the ruler of the the three gunas of Satva, Rajas and Tamas; and sun, moon and fire – the zodiac and the planets, and therefore Time itself.
Om ha sa ka la hrim sodasyai namah
Bhuvanesvari: Means the "Queen of the Universe", Maya, power of love, peace within, as void. She is like the red rays of the rising sun, with the moon as her diadem, and with three eyes, a smiling face, bestowing boons, holding a goad, a noose and dispelling fears. On the right side of Bhuvaneshvari, who in the heavens, on earth, and in the underworlds is known as the Adya, worship Tryambaka.
Om Hreem Bhubaneswaraye Hreem Namah
Bairavi: Bhairavi is Supreme Energy, Supreme Goddess of speech, as Tapas, as woman warrior. Her head garlanded with flowers, she resembling the red rays of 1,000 rising suns, smeared with red, holding milk, book, dispelling fears and giving boons with her four hands, large three eyes, beautiful face with a slow smile, wearing white gems.
Om Bhairavi Saham
Chinnamasta: Chinnamasta is associated with the concept of self-sacrifice as well as the awakening of the kundalini. She is considered both as a symbol of self-control on sexual desire as well as an embodiment of sexual energy, depending upon interpretation. She symbolizes both aspects of Devi: a life-giver and a life-taker. Her legends emphasize her sacrifice – sometimes with a maternal element, her sexual dominance and her self-destructive fury.
Om Shrim Hreem Hreem Aim Vajra Vairochaniye Shrim Hreem Hreem Phat Svaha
Dhumavati: The colour of smoke, wearing smoky clothes, holding a winnowing basket, dishevelled clothes, deceitful, always trembling, with slant eyes, inspiring fear, terrifying. Dhumavati is said to manifest herself at the time of cosmic dissolution and is "the Void" that exists before creation and after dissolution. While Dhumavati is generally associated with only inauspicious qualities, her thousand-name hymn relates her positive aspects as well as her negative ones. She is often called tender-hearted and a bestower of boons
Dhum Dhum Dhumavati Swaha
Bagalamukhi: “The Crane-Headed One”. This bird is thought of as the essence of deceit. She rules magic for the suppression of an enemy’s gossip. These enemies also have an inner meaning, and the peg she puts through the tongue may be construed as a peg or paralysis of our own prattling talk. She rules deceit which is at the heart of most speech. She can in this sense be considered as a terrible or Bhairavi form of Matrika Devi, the mother of all speech
Om Hleem Sarva Dusthaanaam Vaacham Mukham Paadam stambhaya jihvyamkilaya buddhim vinaashaya Hleem Om Swaha
Matangi: The "Tantrik Saraswati", the patron of inner thought and speech. She guides her devotee to the uncaused primordial sound. Matangi has three eyes and either a dark emerald or dark blue complexion. Her mantra includes seed syllables for the manifestation of the Great Goddess in the world, attainment of all desires, protection by the sacred fire (destroys negativity and provides grace), sound that disrupts threatening forces and liberation from the world
Om Hreem Aim Shreem Namo Bhagavati Ucchisthachandali Sri Matangeswari Sarvagyanavashamkari Swaha
Kamala: The "Tantrik Lakshmi", the name Kamala means "she of the lotus" and is linked with three important and interrelated themes: prosperity and wealth, fertility and crops, and good luck during the coming year.
Hasauh Jagatprayutai Swaha
The eight mothers emanate from Devi within the Mahatmyam, each holding different weapons and within different forms. Each go forward into battle, totally destroying the legions of asuras. The Matrikas also guard the corners of the Sri Yantra, the Yantra of Lalita, and thus they can be approached through it.
Brahmi - is Brahma's Atma Shakti - Saraswati, who symbolizes creativity in all forms, music and knowledge. In all efforts that improve the quality of life in this direction, for education, learning and creativity, worship of Brahmi is recommended.
Om aim hreem sreem am aam souh Brahmi maatre kama sanjeevanyai namah
Maheshwari - is the Goddess of Shiva, who represents Mahat Tatwa. She brings Mahat Tatwa under control. So, for those who aspire greatness, through any means, through business or enterprise in various forms, which need insistence on the right things being done at the right time by the right people and the insistence that the things should not be done in the wrong ways and where it needs a little bit of aggression to preserve the competitive edge. For such actions, propitiating Maheshwari is recommended.
Om aim hreem sreem am aam souh Maaheshwari maatre krodha naashinyai namah
Kowmari - is the Atma Shakti of Kumara, Skanda - Ganesha's brother, whose wives are Valli and Devasena. He is Shanmukha, the Kundalini Shakti itself. He resides at all the six chakras balancing them and he is the leader of the armed forces of the Devas. He is also related to Naga Dosha, because Kundalini is serpent power. By propitiating Kowmari by worshipping the Yoni, the seat of Kundalini as Nagashakti, wellness hormones are generated. Conditions suitable for conception are created thereby. So worship of Kowmari is recommended for couples who want to get santana or progeny.
Om aim hreem sreem am aam souh Kowmaari maatre lobha naashinyai namaha
Vaishnavi - She is the Shakti of Vishnu, whose nature is Maya. Maya means Hreem kAra. It is involvement in the world. So Vishnu's Atma Shakti, Vaishnavi who is one form of Lakshmi, creates these illusions of Samsara, is best for improvement of one's relationships in life. There is a relationship between husband and wife, between friends and all kinds of relationships. For improvement in the quality of relationship and establishment of harmony, propitiating Vaishnavi would be very useful.
Om aim hreem sreem am aam souh Vaishnavi maatre moha naashinyai namaha
Varahi - is the commandant of armed forces of Lalita Devi. Residing at Ajna chakra, she is able to give a command, ajna, to various armed forces to quell the enemies. Although it can be used for negative purposes, the positive use of Varahi is to treat the various diseases and internal enemies like kama, krodha, lobha, moha, mada and matsarya and they have to be brought under our control. So, Varahi can be used effectively for controlling the diseases and improving the quality of life. It can be done for the sake of others also by chanting Sankalpam with their names and doing Japa or Prokshana of Varahi Mantra, and relief will be there for the person. It would be especially useful for the application in respect of bringing relief to terminally ill patients, like for those suffering from Cancer and Aids.
Om aim hreem sreem am aam souh Vaaraahi maatre mada naashinyai namaha
Mahendri - is Indra's Atma Shakti. Indra is the God of Rain. He sends his thunderbolt, Vajra to seed the clouds and bring the rain, which fertilizes the earth. So, all our desires regarding the well being of crops, controlling the floods, natural calamities, anything related to rain and water and fertilization of the earth is best handled by worshipping Indra's Atma Shakti - Mahendri. It protects the crops and gives better dairy products and is useful for the people in the agro industry. It is also useful for environmental control.
Om aim hreem sreem am aam souh Maahendri maatre maatsarya naashinyai namaha
Chamunda “Chamunda Shava Vahana” - she lives in cemeteries, rides on corpse, bringing into life. Propitiating this war Goddess Chamunda, who is a form of Chandi, absolutely controls all evils done to you and eliminates that evil. Chamunda is helpful for this.
Om aim hreem sreem am aam souh Chamunda maatre papa naashinyai namaha
Mahalakshmi -Mahalakshmi is the wealth of Sri Mannarayana. She is the cosmic awareness, which shuns the pettiness in every aspect. So, she represents the infinite wealth of the Lord and removes poverty of all kinds. Ashta Aishwaryas and Ashta Lakshmis - are all under her control and they all obey her commands. It is appropriate to propitiate her to get a feel for the spiritual wealth of the Lord. She not only gives material benefits, but also gives the right frame of mind to take you to the oceanic, infinite antaryami consciousness of the Lord.
Om aim hreem sreem am aam souh Maha LakshmI maatre aishwarya keertyai namah