Counterexamples are, for some, crucial in the understanding of a piece of mathematics. They reveal the need for otherwise seemingly ad hoc hypotheses and can also have, in their own right, some of the aesthetic value that is sought for in theorems.

The books *Counterexamples in Analysis *and *Counterexamples in Topology, *which of course inspired the name of this blog, I found to be most helpful in learning analysis and topology. There is no such book for Algebra. This is not because algebra lacks fun counterexamples, but because nobody has sat down, written and published such a book. I hope counterexamplesinalgebra helps fill this gap.

Myself, I am not an algebraist proper. In 2017, I begin a DPhil in Geometry at Lincoln College, Oxford. I will study symplectic and complex geometry *with algebraic techniques. *Higher algebraic structures are especially close to my heart and I plan to write more about them in the future.

Jacob A. Gross

Pittsburgh, PA