An investment theory called the efficient market hypothesis (EMH) claims that it is impossible to outperform the market, and therefore, stocks always trade at a fair value. An important assumption of EMH is that all investors make decisions rationally, without any emotional bias. Despite its wide use, EMH struggles to explain why certain types of investments perform better than others, particularly in liquid financial markets (i.e., the stock market). Since the mid-1980s, some have proposed that this is because liquid financial markets are not always as orderly as is assumed by the efficient market advocates. The best explanation for this is the "noise trader" theory of Black [1] and Delong [2], which posits that if some investors trade on a "noisy" signal, asset prices will deviate from their intrinsic value. Examples of noise include investor behavior, news, and social media. Behavioral finance is a new field that specifically studies the cases where non-rational sources cause the classical financial theory to fail.In this thesis, we investigate the relationship between Twitter and the stock market. To do this, we needed to create a novel training dataset of financial tweets with labeled sentiments. We first used Mechanical Turk to generate a small set of financial tweets, and then designed finance-specific models (using a combination of natural language processing and deep learning) that could accurately predict the sentiments for a much larger set of stock market tweets that span three years. Our final model has an accuracy of 92.7%, which is substantially better than other comparable models. To determine if there is a causal relationship between the sentiments expressed in tweets and the stock market, we applied Granger causality and Bayesian Probabilistic causality models to our new dataset. We found that there is a significant causal relationship between tweets and a company’s stock return at a lag of three hours and one day. Knowing this, it could help investors modify their investment strategies totake into account sentiments expressed in social media.