The Advantages are:
Leads to effective, strong and stable government
Provides a clear link between MPs and their constituents
Prevents a minority party holding an excessive amount of power. This was the case with the Free Democrats in Germany throughout most of the post-war era, because they effectively decided which of the main parties they would join in a coalition
Third parties that concentrate support in a particular area often do well under FPTP (e.g. Plaid Cymru the SNP)
Easy to use and widely understood amongst the electorate
The UK’s parliamentary system is widely respected, and FPTP is undoubtedly a part of that.
The Disadvantages are:
Unrepresentative of the electorate’s wishes
Encourages two party system. Discriminates against the Liberal Democrats. In 2005 they secured 22% of the vote, but gained around 10% of the seats
Governments often fail to gain a majority of the votes. Last time a government gained over 50% was in 1935
Can encourage tactical voting
Creates artificially big majorities – sometimes known as the ‘winner’s bonus’
Government can be elected with less votes than their nearest rival (as was the case in 1951 and February 1974)