Start with building a regular SMPS... maybe a MPPT charge controller for the panels. Read up on SMPS design. I've been interested in it myself and reading about it on and off, but my lack of math skill does make it hard to understand most of it. There is a lot of math involved in designing power supplies. Especially in the magnetics. How big of a core you need, how many turns, etc.
From my understanding so far an inverter is going to be very similar to a SMPS, except you vary the voltage in a controlled way to create the sine wave. So instead of monitoring the voltage and trying to keep it at a constant number, you vary it at a specific time interval to get the 60hz you need. The design is also going to need to be capable of going negative, which is a bit more tricky. A buck-boost topology may work for this, or two separate PSU circuits working together.
You could also start with a square wave inverter, like UPSes, just as a start.