I want to know that when does the classes for grad school begin in US universities. Is it divided into two like summer and fall as i have seen in the websites of universities or does it have a specific month ?
The US does not have a national educational system. Every university determines its own academic schedule. However, there are some similarities. Most universities operate on the "semester" system with two longer semesters and a shorter summer session. The two terms usually start in late August or early September, and in early or late January. Summer term begins near the first of June. There are universities, however, on the "quarter" system, with four equal length quarters. One starts in early January, typically, and they last a bit less than three months.
For graduate study, a student normally begins the academic year in August-September, but can probably begin at the start of any term. Some of the coursework, however is more than one term in length, so you need to be aware of prerequisites for any course.
To be certain, you need to read the admissions materials of each university separately. Many universities will also have a non-academic advisor that you can speak with who will have the answers to such questions. This is part of the admissions system and separate from academic advising.