The things that philosophers study under the heading of "logic" are quite varied. They can be informal or formal, natural-language-based or algebraic.

These books are, necessarily, quite technical, but they do build into a sort of course that could be suitable for self-study.
An Introduction to Formal LogicPhilosophy of LogicsFrom a Logical Point of View
An Introduction to Formal Logic
by Peter Smith
£14.31
Good first course in formal logic, very easy self-study book.
Philosophy of Logics
by Susan Haack
£24.69
Nice overview of the philosophical issues raised by logic. Suitable for beginners.
From a Logical Point of View
by WV Quine
£14.14
A bit antiquated and quirky (Quine always is), so approach with caution.
The Blackwell Guide to Philosophical Logic (Blackwell Philosophy Guides)Mathematical Logic: Part 1: Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems: A Course with Exercises: ... Calculus, Completeness Theorems Pt.1Mathematical Logic: Part 2: Recursion Theory, Godel's Theorems, Set Theory, Model Theory: A Course with Exercises: Recursion Theory, Godel's Theorem, Set Theory and Model Theory Pt.2
The Blackwell Guide to Philosophical Logic ...

Huge and sometimes quite technical; a good handbook, but you might need to supplement it.
Mathematical Logic: Part 1: Propositional C...
by René Cori
£42.75
Excellent advanced course for those with some mathematical background. In two volumes.
Mathematical Logic: Part 2: Recursion Theor...
by René Cori
£42.75