There is lots of interest these days in space exploration. After fifty years we are looking at going back to the Moon to build a base and early planning for a manned trip to Mars. After that, further exploration and settlement of the Solar System will be on the table. One of the main limiting factors for all of this space exploration are the types of rockets and rocket engines available to get there. Current rockets in usage are mainly chemical rockets with fairly low specific impulses. We will need a lot more powerful options to reach all of these destinations. This book is about the history of rocket engine development, what we are using today, and some options for the future. We also discuss some exciting thinking about how we could build interstellar and faster than light space propulsion for exploring the nearest stars too.