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My recommended technique, validated by several others, is to start with Meyers' "Effective C++" and refer back to a primer or the ARM when you don't understand something. This forces you to confront the most jarring and dangerous c++ issues early and helps prevent learning bad habits. As in learning any new language, it helps immensely to be working on a realistic project.
Effective C++ : 50 Specific Ways to Improve Your Programs and Designs (Addison-Wesley Advanced Windows Series) by Scott Meyers
Very readable, full of simple recipes for adapting from C to c++ or avoiding common mistakes in c++. I think any serious c++ programmer should be capable of understanding this book.
Paperback (256 pages, 2nd Ed.). Published by Addison-Wesley Pub Co, September 1997. ISBN: 0201924889
More Effective C++ : 35 New Ways to Improve Your Programs and Designs (Addison-Wesley Professional Computing Series) by Scott Meyers Paperback (318 pages). Published by Addison-Wesley Pub Co, December 1995. ISBN: 020163371X
The Annotated C++ Reference Manual by Margaret A. Ellis, Bjarne Stroustrup
The reference manual that describes every quirk of the language - the sort of thing you must quote if you want to pick an argument with compiler writers
Hardcover (447 pages). Published by Addison-Wesley Pub Co, June 1990. ISBN: 0201514591
C++ Primer by Stanley B. Lippman, Josee Lajoie
A rather long-winded primer. If you like succint explanations avoid this and just buy the ARM, but have a look in at it the bookstore first. It's a very good introductory book and worth dropping back to if you find the others heavy going.
Paperback (1237 pages, 3rd Ed.). Published by Addison-Wesley Pub Co, April 1998. ISBN: 0201824701
Advanced C++ Programming Styles and Idioms by James O. Coplien
You need to be very competent in c++ to understand this book but it presents some interesting techniques, particularly if you're into more dynamic designs that normally associated with c++. I found it a great thought-provoker while designing the framework.
Paperback. Published by Addison-Wesley Pub Co, September 1991. ISBN: 0201548550
Scientific and Engineering C++ : An Introduction With Advanced Tecniques and Examples by John J. Barton, Lee R. Nackman
The examples are definitely SciEng oriented but the descriptions of advanced c++ techniques are superb, more readable than Coplien and well-illustrated with diagrams. The emphasis on templates is probably due to the difference between Coplien as a 1992 book and this in 1994. A great starting point for ex FORTRAN and C programmers.
Hardcover (671 pages). Published by Addison-Wesley Pub Co, July 1994. ISBN: 0201533936
C++ and C Debugging, Testing, and Reliability : The Prevention, Detection, and Correction of Program Errors/Book and Disk by David A. Spuler
A successor to Koenig's "C Traps and Pitfalls" this book combines a list and set of debugging resources with a very clear list of common c++ errors. Some overlap with Meyers' 50 rules occurs, but generally the errors listed are lower level simple bugs.
This title is out of print. ASIN: 0133081729
C++ Iostreams Handbook by Steve Teale
The only detailed and clear explanation of IOStreams that I've seen or seen mentioned. The book documents the older AT&T streams library so there have been a few minor changes but it is still largely applicable and makes a clear case for moving to streams.
Paperback (369 pages). Published by Addison-Wesley Pub Co, August 1993. ISBN: 0201596415
Taligent's Guide to Designing Programs : Well-Mannered Object-Oriented Design in C++ by Inc. Taligent
An internal style guide that grew. Very good advice on structuring libraries to minimize impact of change.
Paperback (152 pages). Published by Addison-Wesley Pub Co, June 1994. ISBN: 0201408880