A proper Lorentz transformation of a vector $\bf{x}$ is given by
$$\bf{x}\to \bf{x}'=\Lambda\cdot\bf{x}$$
where $\Lambda$ is a matrix with the properties
$$\Lambda^T\cdot\eta\cdot\Lambda=\eta~~~,~~~\det\Lambda=1,$$
where $\eta=\text{diag}(-1,1,1,1)$ is the Minkowski metric.
What is a convenient parametrization of all the individual components $\Lambda_{ij}$ of matrix $\Lambda$ for a generic proper Lorentz transformation continuously connected to the identity?