The project deals with the factorization problem in the context of Hopf algebras and other related fields (such as Lie/Leibniz algebras or Poisson/Jacobi algebras). Roughly speaking, the factorization problem for a given structure (i.e. group, Hopf algebra, Lie algebra etc.) can be stated as follows: for two given objects A and B of a category C, describe and classify all objects X which factorize through A and B, i.e. X can be written as a product of A and B, where A and B are subobjects of X having minimal intersection. Of course, the meaning of the words product and minimal intersection depends on the nature of the category C. For instance, if C is the category of groups then a group X factorizes through two subgroups A and B if X=AB and A∩B = {1}. Aside from being of interest in its own right, the study of the factorization problem contributes to the classification problem of finite objects (i.e. groups of a given order or associative/Lie/Poisson/Hopf algebras of a given dimension etc.) as well. The project will focus on several aspects related to the factorization problem and has two general objectives each of them with several open questions. Our first objective refers to the factorization problem in the context of Hopf /Lie algebras as well as other related structures such as Leibniz or Poisson/Jacobi algebras. The second objective concerns the classifying complements problem which is in some sense a sort of converse for the factorization problem. If A is a subobject of X in C, an object H of C is called an A-complement of X in C if X factorizes through A and H. The classifying complements problem asks for the description and classification of all A-complements of X. We will approach the classifying complements problem for Lie algebras as well as for weak Hopf algebras.