Hansard is the official record of what has been said* in both Houses of Parliament. As such it carries a "substantially verbatim" report of proceedings. There are two separate sequences for the two houses. All bound volumes of Hansard are on the open shelves in the Ford Collection on Level 3 of the Hartley Library.
As a record of all that has been said, it can be a valuable tool for understanding the intent behind legislation (see Pepper v Hart box below) and for getting a sense of the mood of the House.
*Hansard also includes Written Answers, Written Ministerial Statements and the record of debates in Westminster Hall. For more on the development of Parliamentary reporting from the 17th Century up to now, see Communicating parliamentary business
Additionally, Public Bill and Standing Committees, which examine the detail of many bills, are also recorded in the same verbatim way, but in separate printed volumes and listed separately via online services. For a little more information on finding these in the Hartley Library and online, see page 14 of our booklet
The first two links below lead to free sources for parliamentary debates, including Public Bill (or Standing) Committees.
Members of this University also have access to two subscription services (House of Commons Parliamentary Papers and Public Information Online) which include Hansard among other official papers.
In the case of Pepper v Hart,  3 WLR 1032, the House of Lords, in their judicial role, established that parliamentary debates could be used in a court of law in order to help interpret ambiguous or obscure legislation. In many instances this will mean consulting the debates of the Standing or Public Bill Committees in addition to the main volumes of Hansard.
For a useful summary on Pepper v Hart, see this Commons Library Standard Note.