The lectures are based on a Tech Report written with Ole Jensen. You'll find pointers to this -- and other things, including the lecture slides -- on my web page www.cl.cam.ac.uk/users/rm135/. I shall begin with examples, including a beautiful one from Cardelli modelling biological membranes. Then I shall give the theory with some precision (but less pain than in the Tech Report), and show how to prove some non-trivial theorems about behaviour; they arose from joint work with Jamey Leifer. In particular, I'll show how Ole Jensen recovered exactly some theory of the asynchronous pi calculus. I shall finish by speculating what a programming language based upon bigraphical algebra might look like; with Danish colleagues I am hoping this may be some use in modelling and designing communications systems that are aware of physical locality.