a modular form is a certain holomorphic function on the complex upper half plane which has an infinite group of discrete symmetries. i will discuss modular forms and some of their generalizations.  in particular, i will try to answer the following questions: what is a modular form? what are some examples of modular forms? what is a simple open question about modular forms?  the examples of modular forms i will give go under the name of "harmonic theta functions".  time permitting, i will describe some exotic variants of these harmonic theta functions that are tied up with the octonions and the compact lie group g_2.