A liquid Cooled below its normal freezing temperature is known as a supercooled liquid. On further cooling, supercooled liquids crystallize to thermodynamically stable, ordered structures. Alternatively, if the cooling rate is fast enough, the crystallization may be avoided altogether. Below a particular temperature during rapid cooling the liquid will solidify into a disordered, amorphous phase -also known as the glassy phase of matter. This particular temperature is termed the ”glass transition temperature” (Tg). Unlike a crystalline solid, a glass is neither a thermodynamically stable phase nor does it possess long range molecular ordering. Very slow structural relaxation (in the time scale of ∼ 100 s) is always present in the glassy phase. Thus, this phase is often referred to as a metastable phase of matter. Experimental and theoretical studies related to the behavior of supercooled liquids are the subject matter of many investigations for the last few decades [1]. These studies find their applications in diverse fields such as geology, cryopreservation, glaciology and atmospheric science. However, properties of supercooled liquids and the corresponding amorphous phase are not completely understood at present, particularly for hydrogen bonded (H-bonded) systems. This thesis concerns both the crystallization and the glass formation process of H-bonded systems. The systems of interest are water, the commonly accepted universal solvent, and the aqueous binary mixture of glycerol and water. The technique of molecular probing is often used to study the cooperativety and rotational diffusion of supercooled liquids and for determination of the glass transition temperature. For the present set of work, a molecular probe technique called spin probe ESR is extensively used. Electron paramagnetic resonance or electron spin resonance (EPR/ESR) measures the electronic energy level separation and is well known for the high sensitivity. All of the systems studied in the present set of work are diamagnetic. This issue is circumvented by dissolving paramagnetic spin probe molecules, which are usually organic free radicals with one N-O group, into the systems. Spin probes are added in very low concentrations (~10-3M) to minimize the effect on the host system and also to avoid mutual interactions between them. The unpaired electron delocalized in the direction of the N-O bond serves as the paramagnetic center required for an ESR experiment. The splitting of electron energy level due to the external magnetic field (Zeeman splitting) can give rise to resonance absorption of energy if exposed to a microwave of appropriate frequency. There is also a magnetic coupling (hyperfine) between the spin of the unpaired electron and nuclear spin of the nearby nitrogen atom. The hyperfine coupling splits each electron energy levels, to the first order, symmetrically into three levels. The transitions between these levels -subject to appropriate selection rules -give rise to the ESR spectrum [2]. The spectral shape in a magnetic field sweep ESR experiment appears complex if randomly oriented spin probes are dispersed in an amorphous or polycrystalline solid matrix. The high degree of mobility in probe molecules, present in a liquid solution, can average out the individual anisotropy of magnetic tensors to get a spectrum of three equally spaced liens. Experiments can be performed spanning a spin probe reorientation timescale of 10-7-10-12 s typically in the temperature range of 4.2 -300K. In chapter one we have given a brief overview of the supercooled liquids and the phase transitions related to the present work. Particular emphasis has been given to the dynamical features of the supercooled liquid close to its glass transition temperature and their classification based on the degree of ’fragility’ [3]. Brief general introductions of the systems studied in each of the following chapters are also provided. Then, the details of ESR spectroscopy and a quantum mechanical picture of the method of spin probe ESR have been discussed [4]. A separate section has been devoted to the numerical and analytical methods used to analyze the spectrum to extract information related to the spin probe dynamics [5]. The chapter concludes with a description of the ESR spectrometer. In chapter two we have studied the glass transition and dynamics of the supercooled water by the method of spin probe ESR. The vitrification has been done by direct exposure of the bulk water sample, doped with the spin probe TEMPOL, to the liquid helium flow. The vitrified matrix turns into the ultraviscous liquid above the putative glass transition temperature of ~136 K which further transforms to cubic ice (Ic) above TX ~150 K. The supercooled fraction of water, along with the spin probes which are treated as impurities by the crystallized surroundings, remain trapped inside the veins or triple junctions of the ice grains which serve as the interfacial reservoir of impurities in a polycrystalline ice matrix. The spectra for the entire temperature range have been analyzed with the help of in-depth computation by modelling the reorientation of TEMPOL in terms of the jump angle θs and the rotational correlation time τ [5]. This model, based on a homogeneous mobility scenario of the spin probe, works nicely except in the temperature range of 140-180 K. Dynamical heterogeneity (DH) is apparent in this temperature range and a more mobile (fast) component, as compared to the one corresponding to the very slow dynamics of TEMPOL at lower temperatures (slow), is observed. The relative weight of the fast and the slow component changes with temperature and above ~180 K the entire spectrum changes into the motionally narrowed triplet. The temperature dependence of the slow component of τ shows a change in slope at a temperature close to the putative glass transition temperature of water. The fast component of τ exhibits a fragile, i.e. non-Arrhenius character at high temperature with a crossover to a strong, i.e. Arrhenius behavior below ~225 K, close to the hypothesized fragile-to-strong crossover (FSC) for water at TFSC ~228 K. The breakdown of the Debye-Stokes-Einstein (DSE) law is observed when the τ values are combined with the available viscosity data of water to evaluate the DSE ratio, paralleling the SE breakdown which has recently been observed in nanoconfined water [6]. The dynamical heterogeneity is thought to be closely associated with the static structural heterogeneities of supercooled water. The existence of large scale structural fluctuations spanning a range of low-and high-density phases of liquid water have been associated with the heterogeneous dynamics sensed by TEMPOL. Motivated by the Arrhenius like behavior of the slow component, it has been identified with the low density liquid (LDL). The fragile nature of the fast component at high temperature may be identified with that of the high density liquid (HDL) which is the predominant fraction in liquid or weakly supercooled water [6]. Chapter three reports the studies on freezing and dynamics of the supercooled water trapped inside the veins of a polycrystalline ice matrix by dissolving spin probes TEMPO and TEMPOL into it. When a millimolar spin probe aqueous solution is cooled below the freezing point of water, the spin probes -driven by the mechanism described above migrate to the liquid environment inside the ice veins. Local concentration of the probe molecules inside the veins can go up to 1-10 M [7]. Bulk crystallization is evident in differential scanning calorimetry (DSC) studies whereas the liquid environment of the spin probe below the bulk freezing is confirmed by its narrow triplet ESR spectrum. A sudden collapse of this narrow triplet into a single broad line indicates the freezing of the trapped water fraction which usually happens well below the DSC freezing point for both the probes. The spin probe detected freezing point of this interstitial water is found to be largely dependent on the properties and the amount of the dissolved probe molecules. An explanation is sought in terms of the ’destructuring effect’ on the tetrahedral ordering of the water H-bond network by both the high local concentration of the spin probes and the hydrogen bond strength, formed between the water and the spin probe molecules through the polar groups of the latter [8, 9]. These two factors are thought to play important roles in determining the reorientational dynamics of the spin probe molecules, as well. The rotational correlation times of the two probes exhibit a crossover owing to the different mobility of their salvation shells in the more ordered supercooled water. The observed relaxation behavior of this confined water using the probe TEMPO, which has little effect on water H-bond network, is found in agreement with the previous experimental investigations on water confined in a nanochannel [10]. In chapter four, the glass transition, relaxation and the free volume of the glycerol-water (G-W) system are studied over the glycerol concentration range of 5 -85 mol% with TEMPO as the spin probe. G-W mixture is intrinsically inhomogeneous due to the well established phase segregation below a critical glycerol concentration of 40 mol%. In the inhomogeneous regime the water molecules tend to form cooperative domains besides the mesoscopic G-W mixture [11]. Samples are quenched by rapid cooling down to 4.2 K inside the spectrometer cryostat. Spectra were recorded on slow heating of the sample in the temperature range of 130 -305 K. The glass transition temperature is correlated to the sharp transition of the extrema separation of the ESR spectrum. The glass transition temperatures are found to follow a concentration dependence which is closely associated to the mesoscopic inhomogeneities of the G-W system. The steady enhancement in fragility of the G-W system with the addition of water is evident from the temperature dependence of the spin probe correlation time τ for the entire concentration range. In the temperature range of 283 -303 K, the DSE law is followed i.e. the spin probe reorientation process is found to be strongly coupled to the system viscosity. In this regime, the τ values have been used along with the available viscosity data to calculate the effective volume V of the spin probe for the entire concentration range. The spin probe effective volume is a measure of the available free volume of the host matrix. A drastic change in the quantity is seen in the vicinity of the 40 mol% glycerol concentration owing to a similar structural change of the matrix due to the formation of mesoscopic scale inhomogeneities below the critical concentration [12]. The thesis concludes with a discussion about the possible future directions of research.