Numbers are the most important of terms in algebraic notation because they, along with variables, are what is being manipulated in equations. You will also come across symbols known as operators, which show the relationship between other notations. The operators include "=" (which means the relationship is equivalent), "+" (meaning that the notations should be added), "-" (subtraction), "/" (division; this is also how fractions are represented) and "*" (multiplication, which can also be expressed by two values next to each other in parentheses).
An especially important notation in algebra is the variable. Variables represent a number that is as of yet unknown. The notation for a variable is typically a letter (for example, "a" or "x"). Variables are treated exactly like numbers, and you can only add like variables to other variables. For example, "a" + "a" is 2a; however, "a" + "b" cannot be further simplified. Additionally, a number placed directly in front of a variable without any further notation is implicitly assumed to be multiplication; "4xy" is a short way of saying "four multiplied by x multiplied by x."
When a number or variable has a small number to its upper right, this is known as an exponent. An exponent is a notation that means to multiply that expression by itself a certain number of times. For example, 4 raised to 3 is another way of saying 4 times 4 times 4, which is 64. Roots are effectively the opposite of exponents, and they put the number or variable underneath a line which looks like a check mark. When taking roots, you find the number that needs to be multiplied that many times to get the value under the root. For example, the √16 is 4 because 4*4 is 16.
Parentheses are a type of notation known as a delimiters, and they are especially important in algebra because they keep unit together called expressions. For example, (4x + 3y) is considered an expression because the "4x" and "3y" are together in the parentheses; without the parentheses, the units would be taken separately when it comes time to solve equations. Additionally, parentheses can sometimes be a shorthand notation for multiplication instead of "*"; for example, (3)(5) is 15.