Algebra 1 covers different types of numbers including real numbers, which consist of rational and irrational numbers and can be thought of as existing on an infinite number line. It also discusses whole numbers as the counting numbers and 0, natural numbers as those first used to count, integers as numbers that can be positive, negative, or zero, rational numbers as fractions or quotients of integers, and irrational numbers as non-repeating decimals that cannot be represented as fractions.