导子和局部导子理论一直是算子代数中的研究热点之一，并且在C^*-代数，von Neumann代数以及非自伴算子代数上取得了大量显著的成果，然而对于无界算子构成的代数上的导子和局部导子，研究的比较晚，所得到的结果相对比较少，非常值得我们做进一步的探索。本项目研究了附属于von Neumann代数的可测算子，局部可测算子以及τ-可测算子构成的代数的性质，进一步将导子理论和局部导子理论全面推广到各类可测算子代数上。我们将深入研究附属于II_1型von Neumann代数的各类可测算子代数上导子与内导子的关系，从而解决Ayupov于2016年提出的问题；将完整刻画附属于真无限von Neumann代数的各类可测算子代数上Jordan导子，Jordan左导子，(m,n)-Jordan导子，局部(2-局部)Lie导子以及可导映射的性质，为研究无界算子代数及其上映射的性质做出有益的探索。

The theories of derivations and local derivations are always one of the research hotspots in operator algebras, and achieved a lot of remarkable results in C^*-algebras, von Neumann algebras and non-selfadjoint operator algebras. However, investigations of derivations and local derivations on unbounded operator algebras began much later, the results obtained are relatively few, it is worth our further exploration. This program focuses on the properties of algebras of measurable operators, locally measurable operators and τ-measurable operators affiliated with von Neumann algebras, moreover, we extends the theories of derivations and local derivations to various algebras of measurable operators. We will make a deep study of the relations between derivations and inner derivations on various algebras of measurable operators affiliated with type II_1 von Neumann algebras, and solve the problem posed by Ayupov in 2016, and we will completely characterize Jordan derivations, Jordan left derivations, (m,n)-Jordan derivations, local(2-local) Lie derivations and derivable mappings on various algebras of measurable operators affiliated with properly infinite von Neumann algebras, make a useful exploration on the research of unbounded operator algebras and mappings.