In this chapter we present a first-principles theoretical and numerical method based on the many-electron algebraic diagrammatic construction [ADC(n)] schemes for electronic excitations, able to describe the correlated multi-electron ionisation dynamics induced in atomic and molecular systems by laser pulses both in the perturbative and non-perturbative regime. Within the ADC(n) framework, electron correlation is described at different levels of approximation depending on the specific ADC method n used within the ADC hierarchy. An accurate representation of the electronic ionisation continuum is achieved by the implementation and computational optimisation of the first- [ADC(1)] and second-order [ADC(2)] schemes in the monocentric B-spline basis set, which makes it possible to describe highly oscillatory discretised continuum wave-functions. The implementation of the time-dependent version of the B-spline ADC method is made by solving the many-electron time-dependent Schrödinger equation via the Arnoldi Lanczos algorithm. As illustrative examples we present applications of this method to the calculations of both static quantities (photoionisation cross sections of noble gas atoms) and dynamical quantities such as the high harmonic generation spectra of Ar and CO2, and the attosecond transient absorption spectrum in laser dressed He atoms.