PROJECT ORION The True Story of the Atomic Spaceship by George Dyson
Of all the insane things that could have been done for spaceflight, this is #1 on my list of things that should have been done. We could have explored the moons of Saturn as early as 1970 and would have a colony on Mars by now.
The price - insanely cheap.
The method - Light a cherry bomb under an inverted garbage can and watch how high it goes. Scale up to 4000 tons (or even much larger) and use very small nukes instead of cherry bombs.
It sounds impossible, but all the engineering problems were well within the capabilities of early 1960's technology. Weight wasn't an issue. They were going to build these things mostly out of steel, possibly at a shipyard. If we built one today (and could find a way around the test ban treaty), it would work even better.
The book goes into great detail about how the idea was developed, how it evolved, and how it was finally killed. In a way, it's too bad it's a non-fiction book. A fictional version would have the project rescued from cancellation and lead to the conquest of the solar system.
Instead, the US and USSR stuck to chemical rockets. The US won the moon race, declared victory, and gave up on human exploration of other worlds (despite repeated promises to get back to the moon or land on Mars "in about 10 to 15 years". Humanity hasn't gone past low earth orbit since December, 1972.
The author of the book is the son of Freeman Dyson. Among many interesting things Freeman Dyson did was working on Project Orion for a few years. Unlike most of the people in the book, he's still alive to be annoyed by the cancellation of Project Orion.