A treatise on field extensions and algebraic extensions

Extension field is the most fundamental concept in Algebraic Number Theory. It plays a vital role while examining the roots of a polynomial equations through Galois Theory. Moreover field extensions are widely used in Algebraic Geometry. This article depicts FIELD EXTENSION THEORY and ALGEBRAIC EXTENSIONS in a recreational way. As this article is written in the current year 2023 and might be published in the year 2024 we have chosen those year’s numbers 2023 and 2024 and made an attempt to demonstrate the central ideas and fundamental concepts of Galois Theory in an elegant apprach.