Yes, it's an alien invasion story, but not like any one you've read before. In the past--perhaps recently, perhaps thousands of years ago, van Vogt is never quite specific--members of several alien races came to Earth, using advanced science to take on the forms of human males. Why? Well, conquest eventually, maybe, depending upon the race--different aliens have different views of the universe and their actions are dictated by their views; some are fairly easy going and fatalistic and others could only be described as mucho macho. Ultimately, though, no matter their natures, the one reason they have all found their way to Earth, infiltrating our society and fighting secret battles amongst themselves, is because they want Earth women. Why? Well, they're not quite sure, because they really don't understand what make women tick. Sort of understandable, when you think about it.
Van Vogt takes the motif of the alien invasion, hypes up a 1950's stereotypical meme (typified by numerous "B" movies and lurid sci-fi pulp magazine covers) and mixes them with themes he explored in many of his previous books--the violent man, repressed American culture, the illogical process of male and female relationships, the inability of people to fully communicate, and the shaping of society by inborn primal natures. As you might expect from the inventor of Dianetics (it's a secret), his forays into science fiction are not at all like those of any other writer, which often causes him to be misunderstood or dismissed. Van Vogt's way of writing is not for everyone--he's always several steps ahead of his characters, who are always one step behind the situation, but one step ahead of the readers. Not an easy read, but for readers up to the challenge it can be rewarding, even this minor book from his later period, when he began to decline.