Best book on philosophy that I know of. But don't get the idea that it's simple: Russell's style is clear, and he is witty, and this can lead readers to think his material is simple; but Russell now and then puts in very sharp and complicated theory-of-types analysis. Its divided mostly into names, which is handy for anyone dipping into the views of Parmenides, Plato, Bacon, Descartes, Locke, Leibniz, Spinoza, John Stuart Mill, Marx, Nietzsche... there's a long list. Russell is happy to admit that academic philosophers have usually been cowardly types, and admits many names (e.g. Byron) not normally considered philosophers.
Russell's style is so convincing he was often plagiarised - unconscious imitation being the sincerest form of flattery. Joad (who copied Russell on Marx), and Aldous Huxley (who based Brave New World on a Russell work) are just two examples.
There are innumerable asides, which I presume (he wrote and assembled this book aged about 70) were the fruit of discussions in his youth and middle age; on psychology, groups, sex, emotions, animals, ethics, totalitarianism, adventures, trade - a vast range of topics.
I recommend this to everyone willing to take some trouble. I've met many people who would have benefitted from its intellectual stiffening - for example a gifted physics man who couldn't seem to grasp that atoms are mostly holes, even though they don't look that way. And who had never understood that the square root of two is 'irrational'. Hoary problems - 'universals', 'analytical' and 'synthetic', 'induction', 'teleology', 'determinism' - appear here and there, and it can do no harm to know about them. Russell also is good at picking out the odd practical effects of beliefs: just one example: Stoics and Christians both believed (supposedly) in personal virtue: if external circumstances cannot prevent a man from being virtuous, there is no need to seek a 'just' social system.
There are omissions, all I think to do with demarcation problems - the boundaries of philosophy, apart from politics, history, science, economics, and psychology. Darwin isn't here (much). Freud isn't here - but then Russell regarded the idea of unconscious motivation as the only significant part of Freud. Adam Smith isn't in. Marx is only treated as a philosopher: his economics is looked at by Russell in another book. Note that Russell seemed to regard Marx as 'socialistic'. All Russell's history in a sense is official: there must be innumerable people who were censored or killed or otherwise silenced; but Russell doesn't really bother with them. His book is a bit like commentary on a tidy, ordered library.
Russell's history is typical 20th century western: prehistory, with Egypt, Babylon and the rest regarded as 'oriental despotisms'. Rather inconsistently, the Bible is admitted. There's a conspiracy of silence about Jewish beliefs. Then Greece, then Rome; then the dark ages, and 'middle ages'; Russell accepts that Islam was a transmitter, though I'm not sure he makes a good case. Finally, modern enlightenment and science. Not much was known about many chunks of history, so this schema appeared satisfactory. Some of his historical comments are typically Victorian: the dislike of Rousseau from hatred of the French revolution, and of Rousseau as the supposed origin of romanticism and silliness. Rousseau and Nietzsche and Carlyle were supposed to have led to extremism and Auschwitz; Plato and Sparta to Stalin.
When eras change, Russell usually finds transitional people or ideas as exemplars: the Greeks treated in the then-usual awed way as a mix of peoples; Christianity as taking in Platonic and Judaic elements; Europe as church vs monarchs and feudal nobility and knights; Machiavelli, Erasmus and More at about the Renaissance. ...
Russell himself doubted his success in describing the relation of philosophy to social events when science became important. Russell mostly knew maths, but was notoriously hopeless in practical activities; he literally couldn't make a cup of tea. Such things as the rise and fall of the idea of phlogiston, the growth of chemistry, changes in transport, and such things as anaesthesia, aren't really covered but taken for granted, in rather the way unreflective people seem to think motor cars and piped water and printing have always existed.
Some accuse Russell of bias; typically these are:-
 Catholics often can't face the rationalistic side of Russell. (They don't seem to know that Russell wrote a lot on mysticism).
 People who like Kant and Hegel, and Nietzsche. Russell was not keen on German philosophy - when he was young, all official philosophers were Hegelians. He followed G E Moore in 'climbing down'.
 Supporters of Wittgenstein. Russell was a friend of his, and liked his work when it was new, but decided later it was rather trivial
 Supporters of Sartre and other existentialists. Russell dismissed it in a sentence: based emotionally on exasperation, and intellectually on errors of syntax.
 'Linguistic' philosophers of the Gilbert Ryle type - 'just another clever man' according to Russell.
Note that, near the end of his life, Russell spent years on the problem of nuclear weapons, Kennedy's assassination, and, later, the Americans and the Vietnam War. For this reason he's partly censored, still.
It's a pity there is no equivalent book on eastern philosophies... Incidentally 'Sophie's World' is based on Russell.