In nature there are millions of distinct networks of chemical reactions 
that might present themselves for study at one time or another. Each new
network gives rise to its own peculiar system of differential equations,
and, to make matters worse, these systems are usually large and almost 
always nonlinear. Nevertheless, each reaction network induces its corresponding
differential equations (up to parameter values) in a precise way. This
raises the hope that, even for highly intricate networks, qualitative
properties of the induced differential equations might be tied directly
to aspects of reaction network structure

Chemical reaction network theory aims to do just that. In particular, it 
aims to place in the hands of those unfamiliar with modern mathematics 
powerful tools for connecting reaction network structure to the capacity 
for various kinds of qualitative behavior.  The theory has not been specific 
to biology, but, for obvious reasons, there is now growing interest in 
biological applications. Very recent work (with Gheorghe Craciun) has been 
dedicated specifically to biochemical networks driven by enzyme-catalyzed 
reactions. It is now known, for example,that there are remarkable and very 
subtle connections between properties of reaction diagrams of the kind that 
biochemists normally draw and the capacity for biochemical switching. My 
aim in this talk will be to explain, for an audience unfamiliar with chemical 
reaction network theory, some tools that have recently become available.