If I said 2,4,6,8,... you would probably say ``10''. Or you might say ``the evens'', or you might give me a program that, on input $i$, outputs $2i$. More generally, if I tell you ahead of time I AM GOING TO GIVE YOU A FUNCTION THAT IS LINEAR and then give you values f(0), f(1), ... you can guess what it is quite easily. In this talk we rigorously define what it means for a set of functions to be LEARNABLE, by which we mean that IN THE LIMIT you can output a program for it. The basic model, and variants of it, will be explored.