No Zone 1
Transport for London would really rather you didn’t travel into Zone 1 – the central part of London. It’s a lot cheaper to travel on the London Underground, or indeed the rail network, if your journey doesn’t involve going to, or through, Zone 1. A Zone 2-3 journey is £1.40 during the Peak Periods, while the same journey on Zone 1-3 is £2.50.
This map (larger version) shows what the tube network (and selected railway lines that go very near Zone 1) would look like, if the Zone 1 stations were taken out. The non-tube/non-Overground/non-DLR lines are shown as black dots. Stations on the boundary of Zone 1 are included as you can travel to these (but not further) without getting the Zone 1 premium.
[As a followup, Here's what happens if you add in bike share docking stations to the mix.]
I’m using a pseduogeographical tube map. It’s based on an original SVG map, collected from public-domain measured coordinates and posted on Wikimedia by Ed G2s and James F, subsequently updated for Wikipedia by David Cane. I then used GEMMA to create a map of all the train lines in London, using the data from OpenStreetMap (CC-By-SA, will be sharing imminently). I then traced over that map in Inkscape to add in the Overground and the selected other railway lines.