= Solution
A <Bravais lattice> is the set of positions generated by integer combinations of independent primitive translation vectors, $\mathbf R=n_1\mathbf a_1+n_2\mathbf a_2+n_3\mathbf a_3$. Every lattice point has the same translational environment. A crystal may additionally have a basis of several atoms attached to each lattice point; those atoms are not automatically separate points of its <Bravais lattice>.
A <unit cell> is a region whose translated copies fill the crystal without gaps or overlaps. It can be chosen for convenient symmetry, and a conventional cell may contain several lattice points. A <primitive unit cell> is a smallest such repeating cell, containing exactly one lattice point when boundary sharing is counted. Its shape is not unique, but its <volume> $\Omega=|\mathbf a_1\cdot(\mathbf a_2\times\mathbf a_3)|$ is fixed for a given lattice. For a monatomic Bravais crystal, each primitive cell contains one atom.
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