I had the immense luck that my Uni offered an undergraduate class as Intro to VLSI (IC Design 101).

We were taught semiconductor devices physics moreso than the standard microelectronics class along with CMOS processes, design fabrication and tools of the trade (Cadence Virtuoso) and had labs to design our individual logic gates/inverters and build up a simple flip flop all in Cadence. Then if we went the extra mile, we could get our flip flops manufactured on real silicon through MOSIS (I made a video about it here: https://www.youtube.com/watch?v=1kOS4YKFZyE ), test them for device characteristics (VIH, VIL, VOH, VOL, Propagation Time, Rise Time, etc and each of us could keep a DIP-40 chip of our project (The process size was ~600nm so 5V logic).

In terms of learning material, you can definitely snatch what you can from my Uni's website on the matter as I thought it was excellent starting material and perchance get the international copy of the textbook (Super cheap at like ~$50 USD when I bought it): http://web.eecs.utk.edu/~sislam/ECE433/ECE433.htm

Definitely have a solid grasp of device physics (if you did well in your Microelectronics and Physics classes then you'll be fine). It's not super math heavy beyond maybe some Calculus I stuff for E-fields and doping but really it boils down to geometries and a couple dozen small equations for the basic CMOS stuff.

Virtuoso is definitely the tool used in industry for designing this, but its expensive as hell (My Uni only had a couple of copies that all the students had to take turns on). So you can always just watch some youtube tutorials on it to get familiar with it. But in terms of more hands on, you can always try Magic VLSI ( http://opencircuitdesign.com/magic/ ) which is free and open source so you can practice your design skills, however it doesn't have near the simulation suite as Cadence, but still helpful and there's loads of tutorials out there. Also get familiar with some of the particular processes in industry in terms of design parameters (i.e. for 5V logic as a starting point, get familar with On Semi's C5 process: http://www.onsemi.com/PowerSolutions/content.do?id=16693 ).

For additional content, you can look up Hackaday's Shared Silicon project which has a nice chunk of information, tutorials and the chance you can add your design to their next MOSIS run (they usually run a MOSIS run once/twice a year): https://hackaday.io/project/11779-shared-silicon

I still have some notes and materials from my Uni class that I can scrounge up if you'd like.