Hastas are hand gestures used in dance.Hasta is a sanskrit word meaning hand.A dancer emotes through her facial expressions, hand gestures and body movements.However a Bharatnatyam dancer cannot hold her hand however she pleases.Hastas and their names,way of holding etc. are specified in the Natya Shastra and the Abhinaya Darpana - the two main books which Indian dancers follow.
There are two kinds of Hastas
1) Asamyuta Hastas - Single hand gestures
2) Samyuta Hastas - Double hand gestures.
And there is another group of hastas called the "Nritta hastas" comprising of a compilation of the others which are frequently used in dance.I give below the original "shloka" of the Asamyuta and Samyuta hastas as i have been taught in Kalakshetra.
Asamyuta Hastas
Pathaakas thripathaako ardhapathaakas kartharimukhaha
Mayuraakhyo ardhachandrashcha araala shukathundakaha
Mushtishcha shikarakhyashcha kapittha katakamukhaha
Suchi chandrakala padmakosha sarpashirasthathaa
Mrigashheersha simhamukhaha kangulashcha alapadmakaha
Chaturo bhramarashchaiva hamsaasyo hamsapakshakaha
Sandhamsho mukulashchaiva thaamrachoodas trishoolakaha
Ithya asamyuta hasthaanam ashtavimshati reerita.
Anjalishcha kapothashcha karkata swasthikasthathaa
Dolahastha pushpaputaha utsangah shivalingakaha
Katakavardhanashchaiva kartari swastikasthathaa
Shakatam shanka chakrecha samputa paasha keelakau
Matsya kurmo varaahashcha garudo nagabandhakaha
Khatwaa berunda ithyethe sankhyaatha samyutaa karaahaa.
Due to paucity of graphics i am unable to give snaps of each mudra.I hope to overcome this soon to provide you with images of all the mudras.