You're right: Shen's mathematical underpinnings (sequent calculus, dependent type theory) can intimidate programmers without a formal logic background. I bought the "The Book of Shen" (TBOS) revision 1 and revision 3. Revision 4 is available on the website. It's a great book with some CS history, logic, and development of Shen from Qi as well as how everything works in Shen including the type system.

Shen uses a dependently typed Sequent-Calculus based Type System (SCTS). It uses type rules vs. type classes, and type checking is optional, you can turn it on or off. Haskell's type inference makes things a bit simpler, and is a battle-tested static type system with excellent type inference which lends itself better for functional programming and large-scale software engineering (for the moment). Shen's TC is more expressive, but requires more effort.

Aditya Siram has some old but goody YT videos on Shen.