This book by Roos et al is one of the best introductory books to interior point algorithms, and certainly offers a novel
introduction, not to be found elsewhere.

The book actually consists of 4 parts. Part I develops
the duality theory for linear optimization, by considering
a considerably simpler self-dual "skew symmetric problem".
This is certainly a novel introduction to interior point methods,
not found in the literature. Part II is based on the usual
logarithmic barrier approach, more in tune with what is known
in the literature, and part III deals with a broader class
of IPM's, some of which not based on "follow the central
path" paradigm. Jim Renegar's famous short step algorithm finds
its place here. Part IV is entitled "Miscellaneous Topics",
and contains a short chapter on Karmakar's famous projective
algorithm.

My only complaint with the book is that since each of the four
parts attempt to be self contained, despite having considerable
overlap, the authors end up repeating the same thing a number
of times, at times annoying!. Anyway, this book is written
by three of the foremost experts in the field of interior point
methods, and if there is one person from whom I would want to
learn IPM's it is Prof. Tamas Terlaky. As the reviewer below
has remarked check out his article on "An easy way to teach
interior point methods" too. To summarize, a extremely
well written book (the authors have put a lot of thought
into this!) and strongly recommended!.

For other books on interior point methods one might want
to check out Wright's "Primal Dual Interior Point Methods",
Ye's "Interior Point Algorithms", and finally Bob
Vanderbei's book (the latter offers only a simple
introduction!).