Probably one of the best general books out there is "Basic Electronics" by Bernard Grob, now in its 10th edition. Although this book addresses all aspects of beginning electronics, it is also a good primer into beginning integrated circuits, especially in the areas of solid-state relays, switches and latches, operational amplifiers, oscillators and timers, opto-isolators, etc. It was my first book in electronics school and still serves as a good fall-back resource. Also look for books written by Forrest Mims III; he wrote many texts on integrated circuits from an experimenter's viewpoint, including the kinds I just mentioned, as well as TTL and CMOS logic. A book on transistor theory will also be an excellent resource as transistors and diodes are the basic components of nearly all integrated circuits.
This next resource might be a bit advanced for some people, but it is still a good reference to have nevertheless. It is "Practical Electronics for Inventors," by Paul Scherz. This book covers a basic refresher for basic electronics, including many of the more-important electrical laws an inventor or engineer needs to know. There are also several chapters devoted to transistors, diodes, op-amps, timers and oscillators, filters, and a section on digital electronics.
If you search on bookfinder.com, you should be able to find clean, used copies of these books. Such textbooks tend to be very expensive brand new, especially to someone on a student budget.
Good luck! I hope these references are a step in the right direction for you.
Personal experience in electronics and Amateur Radio.