Enpō, Kanbun, Meireki, Tenna…

I'm reading the excellent book, 'The Dog Shōgun' by Beatrice M. Bodart-Bailey. Peppered throughout the text are various dates preceded by what appear to be a mini era names and a number; Enpō 3, Kanbun 5, Meireki 1…etc. I can't seem to find a reference to these and/or preferably a list of them for me to learn (I learn stuff like this as a cognitive 'brain exercise').

Can anybody tell me about this dating system?

Here's the list.

Great! I'll stick to just the Tokugawa sub eras since there an awful lot to try and remember otherwise!