Depending on the country of your nationality and also what you intend to do in Ireland, you may need to apply for a visa. If you are a citizen of an EU country and have a valid passport issued by that EU country, then you will not need a visa for Ireland.
Citizens of some non-EU countries can also visit Ireland without a visa for tourism purposes, for stays of up to 3 months.
If the country of your nationality (and of your passport) is listed on this page: http://www.inis.gov.ie/en/INIS/(List%20of%20Countries)%20S.I%20345%20of%202011%20Schedule%201.pdf/Files/(List%20of%20Countries)%20S.I%20345%20of%202011%20Schedule%201.pdf, then you do not need a visa to enter Ireland.
If the country of your nationality (and passport) is not on the list of countries on that page, then you do need to apply for a visa. All visa applications for Ireland must be done online at: https://www.visas.inis.gov.ie/avats/OnlineHome.aspx.
If you intend to work in Ireland and if the country of your nationality and passport is not an EU country, then you will also need to apply for a visa for Ireland. Information on the different types of visas for Ireland is available on this webpage: http://www.inis.gov.ie/en/INIS/Pages/Visa%20Types.
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