Molecular Genetics - the study of genetics at the molecular level
Why? - evolution - unraveling the genomes of various organisms has shown the remarkable similarity and differences between species at the gene level
Medicine
$$$$ - knowledge of the human genome holds great promise for the advancement of medicine
i.e. - some genes give individuals and sometimes whole families a predisposition to a particular cancer or other disease ...... genetic counseling could assist with family planning or even treat diseases by repairs to genes or the proteins they code for that are faulty.
Agriculture - the ghost of Malthus haunts mankind ..... can genetic engineering help create greater yields through a variety of methods (won't the population grow along side)
frost free plants, self fertilizing plants, plants with new colours and flavors that ripen on demand (what about allergies)
Forensic science
-  use of genetic samples can assist the legal industry ascertain identity of alleged perpetrators and disqualify others who are or could have been falsely accused or  convicted.
Nutraceuticals -  perhaps the human gene could be placed inside a banana or potato and diabetics could thus eat a vegetable or fruit each day instead of injecting
Fantasy - Jurassic park , restoration/preservation  of extinct or endangered species (many low tech answers to the latter , X eugenics X , sports
                                "we are a product of evolution not directed evolution"

History
 

Friedrich Miescher was born in Basel on August 13th, 1844. In 1869, he discovered the nucleic acids, the molecular substrate of the genetic code. The work was done in the laboratory of Felix Hoppe-Seyler, which was located in the castle of Tuebingen.
Hammerling 1930  determined that the nucleus was the seat of the cells hereditary material by using the experiments with the single celled acetabularia .

The nucleus was located in the foot of the acetabularia allowing decapitated heads but not feet to regenerate. Different species could not be grafted as could the same species.