Second Foundation is third book of original Foundation trilogy. There are more Foundation books but those are written later. This book concentrates of Second Foundation. When Foundation was founded second hidden foundation was founded same time. First Foundation was formed publicly having all kinds of scientists except people who understood psychohistory. Those people were sent to second Foundation which was meant to work in secret.
Both stories tell about searches of Second Foundation. First continues the Mule’s story. The Mule wants to find mysterious Second Foundation. Second story happens after The Mule’s time. Foundation have recovered and start take interest of search for Second Foundation it sees as threat to it. There are rumors of Second Foundation stopping the Mule.
Second Foundation returns to tones of first book where the goal was to outsmart the opponent. Foundation and Empire told there is nothing you can do to change history. Maybe limits of psychohistory came at the end of first book when First Foundation didn’t social scientist to review it. Mental control of The Mule is also here. Unlike The Mule Second Foundation want to stay hidden and not to rule. Just set things moving to correct direction.
Goal of Foundations was to shorten dark age to thousand years. Original trilogy doesn’t end at end of dark age. It ends at point where there is little to tell without telling same stories again. First book was like history of Europe from fall of Rome to modern day. That road was taken to its end. So second book took different approach which ended fall of Foundation under mental powers of the Mule. Third book is about secret society of mental supermen working behind the scenes. It tells what there is to tell about that. Original trilogy ends when there is nothing more to tell without repeating what was told before. There is one element which reminded lot about one story from the first book. Maybe that was sign to end the trilogy.
I am not familiar of later Foundation books. Don’t know if they get to end of dark age or not. They were written because fans and publisher wanted more Foundation. Those who read the books when they were published had to wait for thirty years for next book. I won’t wait that long but I will have break from Foundation. There are other worlds to explore before I get back to Foundation.