Textbook in PDF format

Learn the basics of algebra from former USA Mathematical Olympiad winner and Art of Problem Solving founder Richard Rusczyk. Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!
How to Use This Book
Acknowledgements
Follow the Rules
Numbers
Order of Operations
When Does Order Matter?
Distribution and Factoring
Equations
Summary
X Marks the Spot
Expressions
Arithmetic with Expressions
Distribution, Subtraction, and Factoring
Fractions
Summary
One-Variable Linear Equations
Solving Linear Equations I
Solving Linear Equations II
Word Problems
Linear Equations in Disguise
Summary
More Variables
Evaluating Multi-Variable Expressions
Still More Arithmetic
Distribution and Factoring
Fractions
Equations
Summary
Multi-Variable Linear Equations
Introduction to Two-Variable Linear Equations
Substitution
Elimination
Word Problems
More Linear Equations in Disguise
More Variables
Summary
Ratios and Percents
Basic Ratio Problems
More Challenging Ratio Problems
Conversion Factors
Percent
Percentage Problems
Summary
Proportion
Direct Proportion
Inverse Proportion
Joint Proportion
Rate Problems
Summary  
Graphing Lines
The Number Line and the Cartesian Plane
Introduction to Graphing Linear Equations
Using Slope in Problems
Find the Equation
Slope and Intercepts
Comparing Lines
Summary
Introduction to Inequalities
The Basics
Which Is Greater?
Linear Inequalities
Graphing Inequalities
Optimization
Summary
Quadratic Equations - Part 1
Getting Started With Quadratics
Factoring Quadratics I
Factoring Quadratics II
Sums and Products of Roots of a Quadratic
Extensions and Applications
Summary
Special Factorizations
Squares of Binomials
Difference of Squares
Sum and Difference of Cubes
Rationalizing Denominators
Simon's Favorite Factoring Trick
Summary
Complex Numbers
Numbers, Numbers, and More Numbers!
Imaginary Numbers
Complex Numbers
Summary
Quadratic Equations - Part 2
Squares of Binomials Revisited
Completing the Square
The Quadratic Formula
Applications and Extensions
Summary
Graphing Quadratics
Parabolas
Circles
Summary
More Inequalities
Quadratic Inequalitie
Beyond Quadratics
The Trivial Inequality
Quadratic Optimization
Summary
Functions
The Machine
Combining Functions
Composition
Inverse Functions
Problem Solving with Functions
Operations
Summary
Graphing Functions
Basics
Transformations
Inverse Functions Revisited
Summary
Polynomials
Addition and Subtraction
Multiplication
Summary
Exponents and Logarithms
Exponential Functions
Show Me the Money
Interesting Problems
What is a Logarithm?
Summary
Special Functions
Radicals
Absolute Value
Floor and Ceiling
Rational Functions
Piecewise Defined Functions
Summary
Sequences & Series
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
Telescoping
Summary
Special Manipulations
Raising Equations to Powers
Self-similarity
Symmetry
Summary
Hints to Selected Problems
Index