An Introduction to Mormonism by Douglas J. Davies.
This is a wonderful book if you are into understanding the more difficult basics of LDS doctrine. Because of its complicated interpretive structure, I have a hard time calling it an introduction. He writes as a University Professor and it shows. Certainly it is the best book on the subject written by a non-Mormon, without clinging to esoterica and other people's misconceptions that usually hurt even the best books on the subject. Even the most celebrated non-Mormon authority Jan Shipps can be too skeptical and careless rather than understanding. This author, however, stays mostly with the authoritative works first, and the others second when needing clarification.
The touch tone of any treatment of Mormonism is how they approach the LDS Temple. I was very surprised and excited that the author rejected sensationalism and expose. He actually talked about the meaning behind the Temple and other related subjects. It is a far cry better than any other similar studies outside the LDS Church. I would recommend reading By the Hand of Mormon by Terryl L. Givens with this book. Both are a compliment to each other.
I would like to mention what I see as a weaknesses in his study. One of the reasons I recommended Givens is that Davies misunderstands the Book of Mormon. Perhaps that is going too far as he does have a pretty good sense of its general message. Rather, Davies doesn't understand the deeper teachings within the Book of Mormon, much less the anticipatory sections that touch on things that will show up later in the Doctrine and Covenants. He reads the Book of Mormon, sadly much like LDS members themselves, from a purely surface reading. That causes him to miss the many subtle and complicated issues it brings up, and dilutes the connections between it and later LDS Scripture. For instance, Davies doesn't sense the deeply ritualistic and priesthood oriented teachings of the Book of Mormon that continually shows up. Examples would be talking about the importance of mysteries, discussions on Melchezidek, mentioning of Priests and Teachers and Twelve Disciples, setting up Churches. Most importantly he misses the discussion of "turning the hearts of the children to the parents" in Third Nephi that Davies makes a big connection with ritual in other chapters of his study. There are other minor quibbles, but they are far less worrisome than what other authors even of the same caliber usually have.
The other book is by an author just mentioned. He doesn't delve into the deep waters of theological exegesis or complicated matters, but what he covers is a worthwhile overview. Again, the main concern is that the purchase prices is too high and a library copy should be sufficient.
The Latter-day Saint Experience in America by Terryl L. Givens.
There isn't as much to say about this book because it doesn't seek to explore any particular arguments. It starts out as a clear narrative of LDS history that covers some controversial events from the Mormon point of view. Yet, it doesn't act as a apologetic so much as clearly trying to present the Mormon understanding of themselves. The history sections alone would be informative to both Mormons and non-Mormons in ways that general writings of one or the other seem to come short.
The second section is more theological and covers the main beliefs. Again, there isn't any deep discussions and yet the information is full of enlightening insights. He sometimes explains misunderstandings that boarder on apologetic, but only when he feels outsiders have misinterpreted key doctrines. His harshest criticism is for those who perpetuate the idea that Mormons hold Christ's Salvation and Grace as of secondary importance. It is clear he holds orthodox beliefs about the LDS Church and its doctrines. That might turn off those who insist on holding their own ideas about Mormons in a negative light. For those honestly wanting to understand the religion, this book is a good start. It is succinct, leaning unbiased for most audiences, and covers a wide range of topics and controversies.