A normal subgroup is a special type of subgroup within a group in abstract algebra. A subgroup H of a group G is considered normal if it is invariant under conjugation by elements of G. This means that for every element g in G and every element h in H, the element g * h * g⁻¹ (where * denotes the group operation) is also in H. Normal subgroups are important because they allow for the construction of quotient groups. The set of cosets of a normal subgroup H in G can be combined to form a new group, denoted as G/H. This process is fundamental in group theory and helps in understanding the structure of groups.