Hello,
I wouldn't recomment The Art of Electronics, at all. Sure, it's an amazing book, but TAOE breezes through foundations and OP says he only remembers Kirchhoff's law.
I think OP wants a book that takes him from there: Tony Kuphaldt's series of books (available for free to download) titled: "Lessons in Electric Circuits".
These babies are 6 books: DC, AC, Semiconductors, Digital.
There's also a book for Experiments where you get the info you need to set up a home lab, and then experiment with the stuff you learned the theory of in the other books.
And a reference book you go to.
http://www.ibiblio.org/kuphaldt/electricCircuits/
The author has also a book titled: "Lessons in Industrial Instrumentation".
"Electronics" is a very vast domain. A lot of reading is needed to itch a specific scratch.
For example, our course about transistors. Yeah, solid physics and band gaps and holes, and manufacturing...
Then after you start using them, you work with "The gain, Beta, is 200". And you go "What makes it 200?"
Like in the manufacturing process, how do you make it that way.
Then you read the late Hans Camenzind's great "Designing Analog Chips" and get to where he explains the influence of the Base thickness.. And you go "Whooaaa". You scratched an itch you had for a long time. The books you read didn't answer that specific question.
Camenzind made the circuit you probably know, NE555. The book is available for free on his site:
http://www.designinganalogchips.com/
Good luck, and if you need anything (resources, etc), feel free to contact me.