Understanding the interaction of matter with ultrashort attosecond light pulse provides fundamental insights into the structure of matter. The electronic properties are reflected in wave packets dynamics. The ability to trace the evolution of electrons in wave packets is a big challenge. It requires ultrashort pulse duration and precise pulse characterization. In this thesis the time-delayed scanning of the atom is used to (1) characterize the inner atomic dynamics, via excitation of the atom by a time-delayed attosecond extreme ultraviolet (XUV) and femtosecond optical field, and to (2) characterize a laser field, via multiphoton ionization of the atom by the autocorrelation function of the field.The first part of the thesis explores the capability of attosecond transient absorption spectroscopy to characterize the dynamics of inner-shell-excited systems. I discuss an unusual kind of pump-probe experiment, where information is gained from the absorption spectrum of an attosecond XUV pulse, which serves as a pump pulse at the same time. The optical pulse in this kind of experiment gives a reference time that provides a possibility to measure the time evolution of a system of interest. In the study, I use different theoretical approaches, treating one or both of the pulses as perturbative or non-perturbative. I present an analytical theory of attosecond transient absorption spectroscopy for perturbatively dressed systems and illustrate how the attosecond transient absorption signal reveals the real-time attosecond dynamics of the atom. In addition, I apply our study to atomic Xe and compare the theoretical predictions with experimental results.In the second part of the thesis a new method for laser pulse characterization is presented. It is based on a machine learning algorithm and is used to study multiphoton autocorrelations in Ar. I analyze the time-delay dependence of the ionization probability for given laser pulse parameters, such as photon energy, pulse intensity and pulse duration. Taking into consideration the mapping between the ionization-probability time-delay pattern and pulse parameters I use a machine-learning algorithm to retrieve the best approximation function for the laser pulse from experimentally measured multiphoton autocorrelation in Ar.