  First principles should predetermine physical geometry and dynamics both
together. In the "algebrodynamics" they follow solely from the properties of
the biquaternion algebra $\B$ and the analysis over $\B$. We briefly present
the algebrodynamics on the Minkowski background based on a nonlinear
generalization to $\B$ of the Cauchi-Riemann analyticity conditions. Further,
we consider the effective real geometry uniquely resulting from the structure
of multiplication in $\B$ which turns out to be of the Minkowski type, with an
additional phase invariant. Then we pass to study the primordial dynamics that
takes place in the complex $\B$ space and brings into consideration a number of
remarkable structures: an ensemble of identical correlated matter pre-elements
("duplicons"), caustic-like signals (interaction carriers), a concept of random
complex time resulting in irreversibility of physical time at a macrolevel,
etc. In partucular, the concept of "dimerous electron" naturally arises in the
framework of complex algebrodynamics and, together with the above-mentioned
phase invariant, allows for a novel approach to explanation of quantum
interference phenomena alternative to the recently accepted paradigm of
wave-particle dualism.
