When I was a student at McGill I loved looking at the latest Springer texts in the now-nonexistant Rosenthall library. So, I thought that I'd list some of the cool looking titles that have come out in 2018:

- Walter Dittrick, Reassessing Riemann's Paper: This book is an analysis of Riemann's paper "On the Number of Primes Less Than a Given Magnitude", and could be a great historical starting point into the subject
- Andreas Hinz, Sandi Klavžar, and Ciril Petr, The Tower of Hanoi – Myths and Maths: Looks like a fun recreational math book about the Tower of Hanoi game
- Wojciech Chachólski, Tobias Dyckerhoff, John Greenlees, Greg Stevenson, Building Bridges Between Algebra and Topology: It contains notes from four different mini-lectures on Hall algebras, triangulated categories, homotopy invariant commutative algebra, and idempotent symmetries!
- Karin Erdmann, Thorsten Holm, Algebras and Representation Theory: Nice-looking text on representation theory. Has classical things like the Artin-Wedderburn theorem and more modern topics like quivers
- V. Lakshmibai, Justin Brown, Flag Varieties: An introduction to flag varieties, assuming some background in commutative algebra and algebraic geometry
- Nicolas Privault, Understanding Markov Chains
- Masao Jinzenji, Classical Mirror Symmetry
- Berthé, Michel Rigo (editors), Sequences, Groups, and Number Theory: Now this looks interesting! It is a curious volume of lectures on the interactions between words (as in formal languages and presented groups), number theory, and dynamical systems
- Ibrahim Assem, Sonia Trepode (editors), Homological Methods, Representation Theory, and Cluster Algebras: A series of lectures from CRM minicourses

*N.B. I do not work for Springer and I do not get compensated for posting these links. I just think they look cool.