What is an interval?
The definition says that an interval is a subset of a set of all real numbers, which is limited from both sides by two endpoints (an endpoint can also be infinity).
Interval is therefore a set of real numbers, which are greater than (or equal to) a given number (or negative infinity) and, at the same time, less than (or equal to) another number (or plus infinity), for instance greater than 5 and less than or equal to 17,(5,17] in mathematical notation. First of all, don't forget that intervals exist only in real numbers.
There are two types of intervals:
Finite interval - the type of interval, which is limited from both sides by given numbers (not by the symbol of infinity), e.g. (-3,2].
These intervals are further distinguished into closed, right-closed, left-closed and open intervals. More details on this in a moment.
Infinite interval - an infinite interval is a kind of interval, which is limited by exact values at most (maximally) on one side, e.g. (-\infty, 1) or (-\infty, \infty).
This type of interval can further be divided, that is, into left-bounded and left closed, left-bounded and left-open, right-bounded and right-closed, right-bounded and right-open and unbounded (this is used rarely) intervals. Although there are many of them, there is nothing difficult about it. A chart showing these types of intervals, which you can find on page 92, will tell you more.