  This lecture consists of three parts. In part I, an overview is given on the
so-called Matrix theory in the light-front gauge as a proposal for a concrete
and non-perturbative formulation of M-theory. I emphasize motivations towards
its covariant formulation. Then, in part II, I turn the subject to the
so-called Nambu bracket and Nambu mechanics, which were proposed by Nambu in
1973 as a possible extension of the ordinary Hamiltonian mechanics. After
reviewing briefly Nambu's original work, it will be explained why his idea may
be useful in exploring higher symmetries which would be required for covariant
formulations of Matrix theory. Then, using this opportunity, some comments on
the nature of Nambu mechanics and its quantization are given incidentally:
though they are not particularly relevant for our specialized purpose of
constructing covariant Matrix theory, they may be of some interests for further
developments in view of possible other applications of Nambu mechanics. The
details will be relegated to forthcoming publications. In part III, I give an
expository account of the basic ideas and main results from my recent attempt
to construct a covariantized Matrix theory on the basis of a simple matrix
version of Nambu bracket equipped with some auxiliary variables, which
characterize the scale of M-theory and simultaneously play a crucial role in
realizing (dynamical) supersymmetry in a covariant fashion.
