van Dalen's Logic and Structure has a chapter on second order logic, but it's only 10 pages long.

Shapiro's Foundations without Foundationalism has as its main purpose to argue in favour of SOL, I've only read the first two chapters which give philosophical arguments for SOL, which were quite good, but a bit too chatty for my tastes. Chapters 3 to 5 is where the actual logic lives, and I can't say much about them.