1. Universal Principles of Design 2nd edition William Lidwell
This book reads as a collection of short one page lessons on various topics of principle. While there is not enough room in such a format to approach most of these topics with much depth, each page contains excellent references for further reading. Overall, it is a useful and very enjoyable book, jumping through all kinds of theories and principles that underline design. If nothing else, I think you would enjoy this.
2. Universal Methods of Design by Bruce Hanington and Bela Martin
This book follows the same format as the book above, but focuses on design ideation and research methods. Not nearly as fun, but a good useful primer on design iteration and research methodologies.
3. The Design of Everyday Things: Revised and Expanded Edition by Don Norman
An excellent primer on how design principles co-relate to everyday experiences. Critically important read for Interactive Design.
4. Information Anxiety 2 by Richard Saul Wurman
The man behind TED, is also considered the godfather of Information Architecture. Collection of articles and ideas related to how we think, learn, perceive and interact with the world. Of this first section of books, this is the only one I would deem optional. A good pre-requisite for Information Design.