An inexpensive handle puller ( looks like a gear puller if you a familiar with mechanics tools) is available.
The outer-most nut you see is a packing nut. To remove the stem for repair or replacement, you need to get a "shower stem socket" which fits down over the inner, larger hex. These tools are also inexpensive and readily available.
The stock at a Depot or Lowes varies regionally. If Gerber is a brand widely used by builders in your area, they might have it. Here in So. Cal. it is all Price Pfister, with a spattering of Delta and Moen It is a common brand, so any plumbing supply will have it.