The science of the classification of organisms is

Taxonomy.

Explanation:

Taxonomy may be defined as the field of biology that mainly deals with the arrangement of the organism. Carolus Linnaeus is popularly known as the father of taxonomy.

Taxonomy includes the classification of the organism and its arrangement in different taxa. The identification, nomenclature and classification of organism is involved in taxonomy. Organisms are classified on the basis of the similarities and differences among them.

Thus, the answer is taxonomy.