The authorship attribution to the Apostle Paul is generally accepted, even among liberal theologians. However, three portions are questioned: 10:1-22 (sometimes) and more commonly 11:2-16 and 14:34-35. The issue with those verses is due to inconsistent manuscript placement: in some manuscripts the verses are at the end of the chapters instead of their traditional placement.
The main topic of the epistle is dealing with issues that had developed in the Corinthian congregation: notable among them are the fragmentation into various groups and the allowance of immorality among the believers.
Chapter 13 is one of the notable chapters in all the Bible, for its constant references to "love" ("charity", in the King James Version).