'One Step From Earth" by Harry Harrison (1970)
is a classic example of the golden age of sci-fi writing, the days of the monthly pulp trade publications like Analog or Isaac Azimov's Science Fiction Magazine which you can come across quite easily at your local used book store or by rummaging through your uncle's basement. I got this little gem for $2 at a used book fair they were holding in the cafeteria at my old call center job and it was worth every penny.
The book is an anthology of related short stories centering around the common theme of a teleportation technology in which enables one to step between two 'matter transmitter' screens, which can be placed at arbitrary points in the universe. Harrison explores the implications of this in a number of ways, illustrating the effect this technology would have on personal relations, warfare, cultural development, crime and criminal investigation, as well as the evolution of the human race.
This is one case in which you can judge a book by it's cover, and in this case the book delivers spacemen, mech tanks, a robot, and cavemen, in equal portions. What more could you want? How about a cop chase though multiple dimension portals. Yup, in there too.
The stories are easily digested (reading in bits as I did, between bouts of having to actually do my job on the phone) and the concepts are built upon from story to story, and set in a coherent and diverse world that Harrison has created. This is one that you can eat up cover to cover in an afternoon or a couple hours commute on the bus or train, and you won't want to put it down once you start.
So go scrounge around your local used book store, or alternatively sites like ebay or amazon regularly have used copies available fairly cheaply.