This is probably Popper's most famous work, in which he lays out his philosophy of science, focusing on the question of epistemology.
The book begins in a surprisingly accessible manner. I was expected some very high level philosophy that would be difficult to understand, but the translation is very easy to follow. Where he gets a little more obscure, he brings it back down-to-earth with examples that help to put his argument in context. I would describe the argument that Popper creates as being cumulative; that is, there are lots of references to earlier sections and, in particular, definitions.
For this reason, I would not recommend reading this book over a long period of time. I think it demands to be read quite intensively in as short a time as possible in order to ensure that one may follow it all.
The main thrust of Popper's argument is to say that theories are never verified, they can only be falsified. He dismantles the positivist point of view which led to empiricism and shows empiricism reduces to mere psychologism. From here, he then needs to discuss the degree of falsifiability. He considers a theory to be less likely the more ways it can possibly falsified. From here, what I think he should have done would then be to talk about corroboration and how a theory stands up to attempts to falsify it. Unfortunately, he leaves this to the end and instead goes off on a rather long and tortuous talk about probability.
This quite long section was the downside for me, as his discussion (and in particular, notation) was quite obscurantist, making it difficult to follow and quite oblique. From here, he moves on to talk about quantum mechanics and in particular the Heisenberg Uncertainty Principle.
This brings me to my last point. If his theory is to be thought of as a scientific theory at all, then it must play by its own rules. That is to say, there must be a set of singular statements from this theory that can, in principle at least, be subject to testing to see if they can be falsified. Such a set of statements is not presented to the reader, so I could only conclude that while Popper's contribution is to be valued and considered, it doesn't constitute a scientific theory. It remains an application of metaphysics.
