Electronic and magnetic properties of quasi-one dimensional ormore widely low-dimensional systems aswell as their related correlated electron phenomena have been at the very frontier of condensed matter physics for quite some time. The reduced dimensionality in these systems offers a unique possibility of direct comparison with model calculations. Furthermore the competing ordered ground states in strongly correlated low-dimensional systems lead to rich phase diagrams comprising many electronic phases, such as superconductivity, charge/spin densitywaves, different electric charge distributions, or a novel formof metalicity. These phases are generically sensitive to a variety of parameters, such as temperature, magnetic field, pressure, a certain degree of irregularity, etc. In this thesis, we employ Electron Spin Resonance (ESR) spectroscopy using strong magnetic fields, high microwave frequencies and high hydrostatic pressure to study a recently discovered family of quasi-one-dimensional organic charge transfer salts, the δ-(EDT-TTF-CONMe2)2X; family to gain insight into the complex physics of strongly correlated low-dimensional compounds. ESR is a highly efficient technique to study organic conductors. This can be easily understood if one realizes that ESR is observable inmost organic conductorswhile only very few "ordinary" metals show detectable ESR signals, even at low temperatures. Indeed, this feature results principally from the electronic low-dimensionality of these systems which controls the spin relaxation process. This tendency is even more reinforced by the fact that most organic molecules only contain light chemical elements for which the effect of the spin-orbit coupling on the ESR linewidth remains small. For this reason, ESR spectroscopy is certainly amajor tool to investigate the paramagnetic state of organic conductors. Moreover, in samples where a magnetic order is present, the large frequency bandwidth of the spectrometers used in the experimental setup (4 GHz–420 GHz) makes the resonance signal accessible at low temperatures in the ordered state, where the resonance frequencywould be too high for conventional ESRspectrometers. Our device hence represents an efficient tool to probe different magnetic ground states and, in particular, the antiferromagnetic state, which is most commonly found in organic salts. Organic conductors exhibit a high degree of sensitivity with respect to magnetic fields and applied pressure. To combine the high sensitivity of the ESR method with the sensitivity and thus fine tuneability of these organic systems by magnetic field and pressure, we build a unique high-field, high-frequency and high-pressure ESR spectrometerwhich is well suited to the study of organic materials. Compared to other devices of its kind, the ESR spectrometer built in our laboratory as a part of this thesis enables a wide parameter space to be explored: magnetic fields from 0 – 16 T, microwave frequencies in the 105 – 420 GHz range and by making use of a custom-made pressure cell, the sample applied pressure can be elevated up to 1.6GPa. To the best of our knowledge, the addition of such a pressure regulating unit to an ESR is unique. Through varying the applied pressure, it can be used to investigate the competition of different ground states: bymodifying the lattice parameters, it can tune the interactions without introducing disorder. The first Part of the thesis is dedicated to a general overview about the physical properties of quasi-one-dimensional organic systems. It also contains a more specific introduction to the crystallographic and electronic properties of the δ-(EDT-TTF-CONMe2)2X family of charge transfer salts. In Part II, we focus on the theoretical description of electronic correlations with a special emphasis on lowdimensional electron systems and on the effect of dimensionality. The objective of this part is to assemble the necessary theoretical notions to understand the phenomena observed in the system under investigation. We show that Coulomb-repulsion in general leads to antiferromagnetism, and give a brief phenomenological description of the antiferromagnetically ordered state. Then, a standard description of the physicalprinciples of Electron Spin Resonance follows. We also give a briefdescription of antiferromagnetic resonance (AFMR) and Conduction Electron Spin Resonance (CESR) with a special focus on quasi-one-dimensional situations. Part III presents the technical details of the ESR spectrometer developed as a part of this thesis. The final Part describes the experimental observations collected during the thesis. In Chapter 9, the phase transitions at atmospheric pressure of a sample of δ-(EDT-TTF-CONMe2)2AsF6 as a function of temperature are presented and discussed. We found a spin-chain behavior at high temperatures and a complicated antiferromagnetic structure below TN=8 K. In the intermediate temperature range we found a suppression of the susceptibility what we explained by the opening of a spin-pseudogap. In Chapter 10, the same procedure is performed for a δ-(EDT-TTF-CONMe2)2Br sample and the findings are really similar to the case of the AsF6 salt. Finally, in Chapter 11, we describe and evaluate measurements performed under high hydrostatic pressure on the δ-(EDT-TTF-CONMe2)2Br sample. We followed the deconfinement transition of the salt and then identified a dimensional crossover from a quasi-one dimensional metal to a more conventional higher dimensional conducting state. At the end of the thesis we drown a general pressure temperature phase diagram of this family of charge transfer salts.