But the standard bible, which is also a great source for beginners, is the Art of Electronics by Horowitz & Hill (just came out with 3rd edition). There's an associated Lab Manual which I also recommend.
AoE stems from a set of lecture notes the authors used in their Physics 123 class at Harvard, which is electronics for experimentalists. I took this class in 1999, AoE was the textbook, and it was amazing. You had people across the spectrum, like psychology and music students, who in about 13 weeks learned from scratch most concepts and components of both analog and digital electronics. The pinnacle of the analog half was one lab where we designed and built a system to take an input audio signal, PWM modulate it as pulses of IR light and flash it across the room to a circuit that received, demodulated, and amplified back to audio. The second half of the class was digital electronics where we started with glue logic and ended by building a breadboard 68000 computer. We programmed it in machine code (they had available external assemblers end EEPROM burners for those of us that wanted to go further). Some students went to amazing depths beyond. Eg, in the Lab Manual they showed some student projects where they took two computer-controlled DAC's and fed them into an oscilloscope in XY mode and made games like PacMan and Asteroids.
Not bad for a one-semester class of students who came in with minimal understanding of electronics.