Cartan's Structure Equations

         We have already use Tensor algebra for constructing General Relativity,that is,Einstein Field Equations.Tensor algebra is useful when we define a physical law in coordinate independend form.However,it is difficult to compute some metric with tensor algebra.So Cartan's Structure Equations allows us very useful and short computations.I will introduce some basic properities of CSE(Cartan's Structure Equatons) here.First of all this text an attempt at writing in english language.Thanks for your tolerance,and please advice me for any mistakes.
Now we will dive into most elegant form of mathematical structure of our universe.
Major motivation of construction of structure equation is transformation of coordinate basis to non coordinate basis.We know from elementary physics only cartesian coordinate is orthogonal.Therefore we want build a framework that have orthogonal basis and independent from chosen coordinate frame.
        To describe a mathematical framework that belong to physical phenomena one has to take a coordinate system and approach a description of experimental fact that valid every time and independend from where experments performed.From this consequences we want orthogonal basis and to be converted between different coordinates.Special relativity and General relativity are coordinate independent theories.And they are valid any referance frame.
        Next chapter we will introduce basics of CSE.