The Incorporation of business is first baby step for any business venture.
For any business or non-business entity, to commence it need to be registered first. There are separate formats available for business inception and separate legislation behind that too.

Private Limited Company
Incorporated under Companies Act, 2013
Public Limited Company
Incorporated under Companies Act, 2013
Foreign Subsidiary
Incorporated under Companies Act, 2013
Branch Office, Liaison Office of Foreign Company.
Separate set of rules by RBI & MCA
Partnership Firm
Under legislation of Indian Partnership Act
Limited Liability Partnership
Incorporated under Companies Act, 2013
Sole Proprietorship Firm
Registration under Shop & Establishment rules of concerned state
One Person Company
Incorporated under Companies Act, 2013
Producer Company
Incorporated under Companies Act, 2013
Trust
Registration under Registration Act, 1908 but conduct governed Through Indian Trust Act, 1882
Society
Registration under Societies Registration Act
Section 08 Company
Incorporated under Companies Act, 2013