Is the Republic of Ireland a part of the UK?

The relationship between the UK and Ireland is a complex one, steeped in history. For centuries, Ireland was under British rule, but after a long struggle for independence, most of Ireland became a self-governing nation. This new nation was initially called the Irish Free State in 1922, and it later became the Republic of Ireland. Northern Ireland, however, remained part of the United Kingdom. So, the key thing to remember is that the UK today consists of England, Scotland, Wales, and Northern Ireland. The Republic of Ireland is a completely separate and independent country with its own government, laws, and currency (the Euro). It's easy to get confused because of the shared history and geographical proximity, but they are two distinct nations. Thinking of it this way helps: the UK is an island, but Ireland is an independent country.
Remember, the UK is only made up of England, Scotland, Wales and Northern Ireland, leaving the Republic of Ireland independent.