Irish Genealogy Resources
Here are some links to some significant research resources for Irish genealogy. While many records have been digitised they have not always been transcribed accurately so to be thorough you should always check the original source and also visit local archives, family history centres, graveyards, libraries etc. Search for typos and other spelling variations of the names you are looking for. It is also helpful sometimes to transpose the first and family names - particularly in census and government records.
There is much value in examining records in context rather than looking at filtered search results because it will help you understand the wider picture but also might lead to breakthroughs via serendipity or observations of broader records. For example, sometimes relatives might get married on the same day - you may not notice this if only looking for one record.
You should be aware that you cannot do comprehensive genealogical research purely over the Internet and certainly not without spending any money. That said, you can start your journey with free online resources.
I would suggest starting with;
Irish Birth, Marriage & Death Records
Irish Genealogy (Free church & civil records provided by an Irish Government project)
Census, Wills, Military and other Records
Books, Reference texts
Guides to History
The Plantation of Ulster (BBC)
Mary Lennon and Ros Davies are deserving of high praise for their genealogical resources.