Ambal's glories are countless. Having said that, none other than Lakshmi Hayagreeva has elaborated her divine qualities in her 1000 names, which was given as an upadesham to Sage Agasthya. The preacher is none other than, Lakshmi Hayagreeva and the student is the glorious Agasthya and thus common loukeekas like all of us will be well benefited by their conversation.
Lalitha Sahasrananam, is like the essence of all the Upanishads, Vedas, Tantra etc.. It has references from Upanishads, Sri Vidya, etc.. and several other granthas. Understand Lalitha 1000 completely may be beyond our scope for one janma - as each of the the methods prescribed there may take several births to understand completely.
But with the graces of our SadGuru, Ambal graces us the divine wealth of Athma Gnanam or wisdom of the Self, which then helps us get enlightened and get a complete context and vision of the verses mentioned in Lalitha 1000.
Glories of Ambal and this glorious verse(s) are uncountable. Lalitha Trishati and Lalitha astotharam, are all the simplified versions of the glorious Lalitha Sahasranamam. Lalithmbal Shobanam is the translated Tamil version of Lalitha Shasranam. But, the Purva Bhagam, PhalaSruti, and the core Lalitha 1000 is the crux of Ambals Vaibhavams, which was taught to Sage Agasthya by none other than, Sri Lakshmi Hayagreeva.