Accidental ignition of flammable gases is a critical safety concern in many industrial applications. Particularly in the aviation industry, the main areas of concern on an aircraft are the fuel tank and adjoining regions, where spilled fuel has a high likelihood of creating a flammable mixture. To this end, a fundamental understanding of the ignition phenomenon is necessary in order to develop more accurate test methods and standards as a means of designing safer air vehicles. The focus of this work is thermal ignition, particularly auto-ignition with emphasis on the effect of heating rate, hot surface ignition and flame propagation, and puffing flames. Combustion of hydrocarbon fuels is traditionally separated into slow reaction, cool flame, and ignition regimes based on pressure and temperature. Standard tests, such as the ASTM E659, are used to determine the lowest temperature required to ignite a specific fuel mixed with air at atmospheric pressure. It is expected that the initial pressure and the rate at which the mixture is heated also influences the limiting temperature and the type of combustion. This study investigates the effect of heating rate, between 4 and 15 K/min, and initial pressure, in the range of 25 to 100 kPa, on ignition of n-hexane air mixtures. Mixtures with equivalence ratio ranging from 0.6 to = 1.2 were investigated. The problem is also modeled computationally using an extension of Semenov's classical auto-ignition theory with a detailed chemical mechanism. Experiments and simulations both show that in the same reactor either a slow reaction or an ignition event can take place depending on the heating rate. Analysis of the detailed chemistry demonstrates that a mixture which approaches the ignition region slowly undergoes a significant modification of its composition. This change in composition induces a progressive shift of the explosion limit until the mixture is no longer flammable. A mixture that approaches the ignition region sufficiently rapidly undergoes only a moderate amount of thermal decomposition and explodes quite violently. This behavior can also be captured and analyzed using a one-step reaction model, where the heat release is in competition with the depletion of reactants. Hot surface ignition is examined using a glow plug or heated nickel element in a series of premixed n-hexane air mixtures. High-speed schlieren photography, a thermocouple, and a fast response pressure transducer are used to record flame characteristics such as ignition temperature, flame speed, pressure rises, and combustion mode. The ignition event is captured by considering the dominant balance of diffusion and chemical reaction that occurs near a hot surface. Experiments and models show a dependence of ignition temperature on mixture composition, initial pressure, and hot surface size. The mixtures exhibit the known lower flammability limit where the maximum temperature of the hot surface was insufficient at igniting the mixture. Away from the lower flammability limit, the ignition temperature drops to an almost constant value over a wide range of equivalence ratios (0.7 to 2.8) with large variations as the upper flammability limit is approached. Variations in the initial pressure and equivalence ratio also give rise to different modes of combustion: single flame, re-ignition, and puffing flames. These results are successfully compared to computational results obtained using a flamelet model and a detailed chemical mechanism for n-heptane. These different regimes can be delineated by considering the competition between inertia, i.e., flame propagation, and buoyancy, which can be expressed in the Richardson number. In experiments of hot surface ignition and subsequent flame propagation a 10 Hz puffing flame instability is visible in mixtures that are stagnant and premixed prior to the ignition sequence. By varying the size of the hot surface, power input, and combustion vessel volume, we determined that the instability is a function of the interaction of the flame with the fluid flow induced by the combustion products rather than the initial plume established by the hot surface. The phenomenon is accurately reproduced in numerical simulations and a detailed flow field analysis revealed a competition between the inflow velocity at the base of the flame and the flame propagation speed. The increasing inflow velocity, which exceeds the flame propagation speed, is ultimately responsible for creating a puff. The puff is then accelerated upward, allowing for the creation of the subsequent instabilities. The frequency of the puffing is proportional to the gravitational acceleration and inversely proportional to the flame speed. We propose a relation describing the dependence of the frequency on gravitational acceleration, hot surface diameter, and flame speed. This relation shows good agreement for lean and rich n-hexane-air as well as lean hydrogen-air flames.