This submission is the first installment in the electronic publication of "EXPLORING NEURAL NETWORKS WITH MATHEMATICA", an extensive collection of instructional Notebooks developed in the last two year to support two Neural Neworks courses at UCLA. This first series covers some basic theory and elementary examples of common neural algorithms. These Notebooks are intentionally informal and strictly stand-alone. They are given to students as starting points for exploration and as initial models for their term notebooks. They do not rely on a deep knowledge of Mathematica. Priority has been given to readability and self-documentation. Within reason, problem variables are given long self-explanatory names. Clever programming tricks are avoided as well as all but the most common opeator symbols. You are free to access these Notebooks and use them at your own risk for any non commercial purpose. For Additional information, contact: Dr. Jacques J. Vidal | University of California | Phone:310/825-2858 vidal@cs.ucla.edu | Los Angeles | Fax: 310/206-5115 | BH 3531, Los Angeles, Ca.| | 90024-1596 |