Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book.
It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles.
Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in the C++ chat room. (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list. Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review.
Beginner
Introductory, no previous programming experience

Author: Stanley Lippman, Josée Lajoie, and Barbara E. Moo (updated for C++11)
Description: Coming at 1k pages, this is a very thorough introduction into C++ that covers just about everything in the language in a very accessible format and in great detail. The fifth edition (released August 16, 2012) covers C++11.
Introductory, with previous programming experience

Author: Bjarne Stroustrup (2nd edition for C++17, 3rd edition for C++20)
Description: The “tour” is a quick (about 180 pages and 14 chapters) tutorial overview of all of standard C++ (language and standard library, and using C++11) at a moderately high level for people who already know C++ or at least are experienced programmers. This book is an extended version of the material that constitutes Chapters 2-5 of The C++ Programming Language, 4th edition.
Best practices

Author: Scott Meyers, 3rd Edition – May 22, 2005
Description: This was written with the aim of being the best second book C++ programmers should read, and it succeeded. Earlier editions were aimed at programmers coming from C, the third edition changes this and targets programmers coming from languages like Java. It presents ~50 easy-to-remember rules of thumb along with their rationale in a very accessible (and enjoyable) style. For C++11 and C++14 the examples and a few issues are outdated and Effective Modern C++ should be preferred.
Related Queries
How can I learn C++ by myself?
Step 1: Prepare Your Technology. There are a few different concepts you’ll need to be familiar with before you start coding. …
Step 2: Master the Basics. …
Step 3: Build a Project. …
Step 4: Join a Free C++ Online Community. …
Step 5: Practice, Then Practice More. …
Step 6: Share Your Work.