I really enjoy the Notices of the AMS “What is…?” articles. They are generally brief perfunctory definitions and material aimed at mathematicians outside of the fields described. I enjoy them for gaining some breadth before diving into articles outside of my repertoire. Here are a list of highlights relating to AT, because they’re a fun place to start reading about these topics.
Equivariant Cohomology– Loring W. Tu
an Infinity Category– Jacob Lurie
a Linear Algebraic Group– Skip Garibaldi
Persistent Homology– Shmuel Weinberger
an Operad– Jim Stasheff
a Projective Structure– William M. Goldman
a Legendrian Knot– Joshua M. Sabloff
a Perverse Sheaf– Mark Andrea de Cataldo and Luca Migliorini
a Stack– Dan Edidin
a Derived Stack– Gabriele Vezzosi
Jean Verrette 