The correct answer is option 1, John Dalton. The atomic theory of matter was first proposed by Dalton in the early 19th century. Dalton`s atomic theory proposed that all matter is made up of tiny, indivisible particles called atoms. He also stated that atoms of different elements combine in fixed ratios to form compounds, and that chemical reactions involve the rearrangement of atoms.

Option 2, Rutherford, is not the correct answer. While Rutherford made significant contributions to our understanding of the atom, such as discovering the atomic nucleus, his work came after Dalton`s initial proposal of the atomic theory.

Option 3, J.J. Thomson, is also not the correct answer. Thomson discovered the electron and proposed the plum pudding model of the atom, but his work came later than Dalton`s.

Option 4, Niels Bohr, is also not the correct answer. Bohr made important contributions to the field of atomic structure, specifically his model of the atom with energy levels, but his work also came later than Dalton`s initial proposal.

In summary, John Dalton was the first to propose the atomic theory of matter, which laid the foundation for our understanding of atoms and molecules.