MAX phases are layered early transition metal ternary carbides and nitrides so called because they are composed of M, an early transition metal, A, a group A element and X is C and/or N. MAX phase structure is composed of near close-packed planes of M atoms with the X atoms occupying all the octahedral sites between them. Their physical properties (stiffness, damage and thermal shock resistance, high thermal and electrical conductivity) along with the fact they are readily machinable, make them extremely attractive in terms of the potential technological applications.In 2011, it was discovered that by immersing Al-containing MAX phases in HF acid, it was possible to selectively etch the Al, resulting in two-dimensional (2D) materials, that were labeled MXene to denote the removal of the A-group element and make the connection to another conducting 2D material, graphene. This new member of 2D materials family owns stronger, more chemically versatile, and have higher conductivity than other materials. As such they are highly interesting on new applications, e.g. specialized in vivo drug delivery systems, hydrogen storage, or as replacements of common materials in e.g. batteries, sewage treatment, and sensors.In this thesis, as its self-telling title indicated, we present our work on the synthesis, structural characterization and the electron transport in the MAX phases and their 2D derivatives, MXenes.For MAX phase: motivated by the theoretically expected anisotropic properties of these layered materials, producing bulk single crystals is a natural way to obtain samples where the anisotropy of the physical properties can be experimentally probed. Also, knowledge of low-temperature behavior of single crystal is vital because it can provide insight into MAX intrinsic physical properties. Using high temperature solution growth and slow cooling technique, several MAX phases single crystals have been successfully grown, including Cr2AlC, V2AlC, Ti3SiC2, etc. Structural characterization confirms the single crystalline character of the samples. Experimentally, a set of experimental data was obtained from single crystals of V2AlC and Cr2AlC as a function of temperature and magnetic field. In particular, we obtain a very high ratio between the in-plane and parallel to the c-axis resistivity, which is very substantial, in the range of a few hundreds to thousands. From MR and Hall effect measurement, in-plane transport behaviors of MAX phases have been studied. The extracted mobility is in the range from 50 to 120 cm2/V·s, which is the same order of magnitude of polycrystalline sample. Theoretically, a general, yet simple model was proposed for describing the weak field magneto-transport properties of nearly free electrons in two-dimensional hexagonal metals. It was then modified to be applicable for the transport properties of layered MAX phases.For MXene: Large scale V2CTx MXene flakes was successfully synthesized by conventional HF-etching of V2AlC single crystals. Mechanical delamination of multilayered V2CTx flakes into few layer flakes and transfer on Si/SiO2 substrate was also achieved. Structural characterization demonstrated an enlarged interplane distance, while prior DMSO intercalation seems to have no effect on this type of MXenes. From EDS results, we concluded that -OH terminations on V2CTx is the dominated, and the most energetically favorable, compared to -F and -O functional groups. We then detail the electrical device fabrication process and proceed with electrical measurements results, performed down to low temperature, with the aim to extract useful information on charge carrier behavior. We successfully obtained some first hand transport data on V2CTx MXenes, the average value for the resistivity of V2CTx MXenes is 2 × 10-5 Ω ∙m, which is in consistent with reported other MXene samples. The mobility, 22.7 cm2/V·s , which stays in the same order of magnitude as its parent MAX phase.