Who was the first king of the Mysore kingdom?

The first king of the Mysore Kingdom was Adi Yaduraya Wodeyar or Raja Vijaya Raj Wodeya. He became the first king by defeating and killing Delavoi Mara Nayaka of Karugahalli, who had usurped Royal power in Mysore

For further reading check the following articles:

• First and Second Anglo-Mysore Wars
• NCERT Notes on Third & Fourth Anglo-Mysore Wars