Absolute matrix summability methods of infinite series

This study consists of six sections. In the first section, it is talked about the purpose of summability, the history, the place and the importence in mathematics. In the second section, basic definitions, the theorems and the lemmas which will be used throughout the study are given. In the third section, a theorem which deal with summability factors and another theorem which generalizes this theorem dealing with summability factors are stated and proved. In the fourth section, a theorem giving the equivalence of the summability methods and and another theorem which analyzed relationship between the summability methods and are stated and proved. In the fifth section, firstly a theorem giving necessary conditions that a series, which is summable , also in order to be summable is stated and groved. Afterwords another theorem giving necessary conditions that a series, which is summable also in order to be summable is stated and proved. In the final section, the aim of the study is supported by giving some corollaries concernig previously proved theorems. Key Words: Summability, Absolute Summability, Summability Factors, Matrix Summability, Riesz Summability Method, Sequence Space.