Please give me a short description of each of the three categories of performance that Bharatanatyam follows.

The repertoire of Bharatanatyam, like all major classical Indian dance forms, follows the three categories of performance in the Natya Shastra. These are Nritta (Nirutham), Nritya (Niruthiyam) and Natya (Natyam).[58]

The Nritta performance is abstract, fast and rhythmic aspect of the dance.[63] The viewer is presented with pure movement in Bharatanatyam, wherein the emphasis is the beauty in motion, form, speed, range and pattern.[58] This part of the repertoire has no interpretative aspect, no telling of story. It is a technical performance, and aims to engage the senses (prakriti) of the audience.[64]
The Nritya is slower and expressive aspect of the dance that attempts to communicate feelings, storyline particularly with spiritual themes in Hindu dance traditions.[63] In a nritya, the dance-acting expands to include silent expression of words through gestures and body motion set to musical notes. The actor articulates a legend or a spiritual message. This part of a Bharatanatyam repertoire is more than sensory enjoyment, it aims to engage the emotions and mind of the viewer.[58][64]
The Natyam is a play, typically a team performance,[10] but can be acted out by a solo performer where the dancer uses certain standardized body movements to indicate a new character in the underlying story. A Natya incorporates the elements of a Nritya.[58]

1. Nritta: This is the pure movement aspect of the dance of Bharatanatyam. The dancer showcases movements in varying form, speed, range and levels. 
2. Nritya: This is the expressive aspect of the dance, wherein the dancer tells a story, usually of a spiritual theme of Hindu tradition, through both facial expressions and movements.
3. Natyam: This is the theatrical aspect of the dance, where the dancer incorporates the elements of Nritya, to enact different characters of a play. This can be performed either solo or as a team.