Here are the Nine Avatars of Maa Durga

The first form of Goddess Durga is called Shailputri . She is considered the daughter of the Himalayas. She is a form of Shakti, the consort of Lord Shiva.

The second form of Goddess Durga is known as ‘Brahmacharini’. Her name is derivative of the word ‘Brahma’, which means ‘Tapa’ or penace. She is also a form of Uma or Parvati, a form of Mata Shakti

On the third day the goddess is worshipped as Chandraghanta. She is the symbolic representation of beauty and bravery

Kushmanda, is the form of the goddess which is worshipped on the fourth day. It is believed that Kushmanda is the creator of the entire Universe and she has created the entire Universe by her laugh

Skandamata is the fifth form of the Hindu Goddess Durga. It is believed that she awards devotees with salvation, power, prosperity and treasures. She can grant oceans of wisdom even to most illiterate person, if he happens to worship her. Skandmata who possesses the brilliance of the sun fulfills all the desires of her devotees

Katyayini is the sixth form amongst the Navadurga,she is associated with the fierce forms of Shakti or Durga, a Warrior goddess, which also includes Bhadrakali andChandika

On the seventh day, the Goddess is worshipped as ‘Kalratri’. As the name suggests, Kalrati is as black as a dark night. She has four hands, she is meant to make the devotees fearless

the Mata Rani is worshipped as ‘Maha Gauri’. She is considered to extremely beautiful, white like snow and accessorized with white colored ornaments. She represents calmness and exhibits wisdom.

On the ninth day, Durga is worshipped as Siddhidatri. It is believed she consists of all the eight siddhis. She lives on lotus and is worshipped by all the Rishis-Munis, Siddhas, Sadhakas and Yogis.

What are the Nine Avatars of Goddess Durga?

Adya Shakti has nine million Avatars:

“ওঁ বন্ধূককুসুমাভাসাং পঞ্চমুণ্ডাধিবাসিনীম্ ।
স্ফুরচ্চন্দ্রকলারত্নমুকুটাং মুণ্ডমালিনীম্ ॥
ত্রিনেত্রাং রক্তবসনাং পীনোন্নতঘটস্তনীম্ ।
পুস্তকং চাক্ষমালাং চ বরং চাভয়কং ক্রমাত্ ॥
দধতীং সংস্মরেন্নিত্যমুত্তরাম্নায়মানিতাম্ ।
য়া চণ্ডী মধুকৈটভাদিদৈত্যদলনী য়া মাহিষোন্মূলিনী
য়া ধূম্রেক্ষণচণ্ডমুণ্ডমথনী য়া রক্তবীজাশনী ।
শক্তিঃ শুম্ভনিশুম্ভদৈত্যদলনী য়া সিদ্ধিদাত্রী পরা
সা দেবী নবকোটিমূর্তিসহিতা মাং পাতু বিশ্বেশ্বরী ॥”
Om. She who is reddish like hibiscus in complexion and is seated on a seat of five skulls; whose crown has a rising crescent moon studded as a gem; who wears a garland of skulls/severed heads and has firm breasts like pitchers; who is three-eyed and clad in red garments; who holds a book, a rosary while displaying the gestures of bestowing boons and fearlessness serially; I meditate upon the that Supreme Goddess of excellent features, whom all Agamic scriptures eulogise.
That Chandika who is the destroyer of Asuras Madhu & Kaitabha and vanquisher of Mahishasura; who is the slayer of Dhumralochana, Chanda & Munda and who ingested Raktabija; who is the Supreme Energy (of Sadashiva) that killed Asuras Shumbha & Nishumbha and bestower of fruits of actions; who has nine million forms/who is served by nine million goddesses, may that Mother of all worlds sustain me.

But since Devi’s Avatars are infinite, we have chosen some important ones who have been given more emphasis in scriptures:-

Dasa Mahavidya:
1) Kali
2) Tara
3) Tripurasundari
4) Bhuvaneshvari
5) Bhairavi
6) Chhinnamasta
7) Dhumavati
8) Bagalamukhi
9) Matangi
10) Kamala

Matrika:
1) Brahmi
2) Maheshvari
3) Shivaa
4) Rudrani
5) Pratyangira
6) Kaumari
7) Vaishnavi
8) Narayani
9) Varahi
10) Narasimhi
11) Vinayaki
12) Aindri
13) Shivaduti
14) Chamunda
15) Kauberi
16) Agneyi
17) Vayavya
18) Saurya
19) Mrityu Devi
20) Varuni

Ashtadurgas:
1) Ugrachanda
2) Prachanda
3) Chandogra
4) Chandanayika
5) Chanda
6) Chandavati
7) Chandarupa
8) Chandika

Panchadurgas:
1) Ekanamsha
2) Shatakshi-Shakambhari
3) Raktadanta
4) Bhima Devi
5) Bhramari Devi

Navakalis:
1) Dakshina Kali
2) Vama Kali
3) Maha Kali
4) Bhadra Kali
5) Smashana Kali
6) Guhya Kali
7) Kamakala Kali
8) Sri Kali
9) Kala Kali

15 Nitya Devis:
1) Kali
2) Kulla
3) Kurukulla
4) Kapalini
5) Viprachitta
6) Virodhini
7) Ugra
8) Ugraprabha
9) Dipa
10) Nila
11) Ghana
12) Balaka
13) Matra
14) Mudra
15) Mita

Other Devis:
1) Jagadhatri
2) Mahishasuramardini
3) Jaya Durga
4) Padmavati
5) Kaushiki
6) Sati
7) Parvati
8) Kamakhya
9) Mahamaya
10) Brahmavidya
11) Gayatri
12) Kalika
13) Vajrayogini
14) Shitala
15) Ganeshajanani
16) Mula Prakriti
17) Karali
18) Kameshvari
19) Mundamardini
20) Bhavani
21) Muktakeshi
22) Asikara
23) Ambika
24) Mundamalini
25) Kula-Kundalini
26) Simhavahini
27) Vindhyavasini
28) Patala Bhairavi
29) Guhyeshvari
30) Sugandha
31) Annapurna
32) Nitya
33) Maha Lakshmi (not to be confused with Vishnu’s consort)
34) Maha Sarasvati (not to be confused with Brahma’s consort)
35) Chandika
36) Ardhanarishvari
37) Lalita
38) Rajarajesjvari
39) Parameshvari
40) Aparna

These are some of the Avatars of Adya Devi that I am familiar with. There are many more, whose names I do not know. I hope some day by Adya Shakti grace I come to know all Her Avatars.