IPO : Primary market offerings

The primary market for equities is the market in which a company issues stock for the first time to the general public (initial public offering) or to private investors (placing). The main method of issuing stock in the primary market is through an initial public offering (IPO).

IPO : Initial public offering

An initial public offering, or IPO, is the first sale of stock by a company to the public. A company can raise money by issuing either debt or equity. If the company has never issued equity to the public, it's known as an IPO.
Although some stocks may be reserved for some special buyers and employers.

See the difference between private and public companies here.

Underwriting Arrangements

Underwriting agreements specify how the underwriter will go about selling the new equity issue. Two of the most common underwriting agreements between the investment bank and the issuing corporation are:

• Firm commitment 
• Best efforts 

Firm commitment
In this case, Underwriter buys entire issue and re-offers issue at higher offering price. Here Investment bank(the underwriter) takes the risk of  selling whole issue, so underwriter enters into agreement only when they are sure that they can sell entire issue. The variant of firm commitment is :
Traditional Underwriting - Here underwriter has market out clause allowing the underwriter to back out if the markets are weak.
Brought deals - Here market out clause is much narrower and underwriter is firmly commited to sell entire issue.
Best Efforts

In a best efforts agreement, the underwriter will use its 'best efforts' to sell as much of the issue as possible. However, the underwriter is not responsible for any shares that remain unsold. The underwriter in a best efforts agreement receives a flat fee due to the lower risk faced. Best efforts agreements are typically used with issues that are harder to sell, such as unseasoned issues.