Bharatnatyam
The dance form is known for its beautiful body movements and gestures which are called Mudras in the traditional language. It focuses on the hand gestures, leg movement and the facial expressions of the dancer.

Kathak
Kathak is performed in the form of storytelling through the body movements used by the dancer. Kathak is often referred to as the dance of love, and it can be performed by both by the male and female dancer together.

Kathakali
Kathakali is one of the most renowned and religious dances forms of India. It originates from the tales of Ramayana and Shiva stories. Kathakali includes the intriguing face movements and the heavy costumes which include the traditional face masks and body paints

Manipuri
Manipuri comes as an important symbol to represent the state of Manipur from the region. This dance form is performed to narrate the romantic relationship between the Hindu gods Radha and Krishna, which is famously known as RaasLeela.

Kuchipudi
Kuchipudi is probably the toughest form of classical dance in India. Kuchipudi includes both singing and dancing by the performer which is why it requires both the skill and much more dedication than any other art forms in India.

Bhangra/Gidda
Belonging to Punjab, Bhangra is a heart-pumping dance adorned with the loud beats of dhol( traditional Indian instrument). Bhangra is another level energetic dance, you dance with your heart out, vibes that cannot match to any another dance form.
Well not only Bhangra there is Gidda as well. So in these what really happens that ladies talk about how their day went and stuffs like that as in a form of singing and dancing in a slow-mo form. It's a pride of Punjab heritage and culture.

Well there are so and so dance forms in India as this country is basically rich and versatile in culture and heritage. But for me, this are the most famous forms of classical Indian dance i know