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	\centerline{\textbf{\small{BY}}}
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	\centerline{\textbf{\small{Sajede Talei Lari}}}
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In the 19th century were discovered new numbers called quaternion and octonion were also employed in physical computing. Because these two sets of numbers respect to multiply do not commute  and octonion do not associative, have interesting applications. In this thesis With the introduction of these two numbers and express their mathematical properties, tried that explain field theory with them. It may be that in some cases we have been able calculate shorter and more compact. For example, in discussing relativity, gravitational and electromagnetic fields using quaternion able to be expressed in one equation. Hope that by using mathematics, physical phenomena to be explained better and easier.
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Keywords: quaternion, octonion, field theory
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