Different kinds of fuzzy subalgebras of an algebra (lattice valued, partially ordered, relational) are defined as the mappings from an algebra to the corresponding structure (lattice, partially ordered set, relational structure), with the property that every level subset is an ordinary subalgebra. Fuzzy congruences are introduced similarly. Every fuzzy subalgebra of an algebra is uniquely determined by a suitable collection of subalgebras and vice versa (the same is with congruences). It is proved that all lattice valued subalgebras (congruences) of an algebra, form an algebraic lattice, independant of the lattice being the codomain of the mappings. The collection of partially ordered and relational valued subalgebras is also uniquely determined by the algebra itself. Some consequences in the case of fuzzy subgroups and normal fuzzy subgroups of a group are investigated. In particular, conditions under which the lattice of all lattice valued fuzzy subgroups is Boolean are given.