Yevamot 44: Rabbi Akiva's Mamzerim

A case: 4 brothers married to 4 women, and some of the brothers died... Can a brother do yibum more than once? When is chalitzah done instead? What does an "invalid" status mean? Also, a man who remarries the woman he'd divorced, after she is divorced or widowed by someone else. Can they stay married? What is the status of children? Note Rabbi Akiva's difficult (and rejected) position regarding who is a mamzer.