This talk aims to expose the audience to a broad introduction of algorithmic and quantitative trading practices by first presenting a brief history of financial markets, introducing the players and the trading instruments (major asset classes) in the financial domain, elaborating the process of trading with generally overlooked details and associated hidden costs, and then comparing conventional trading methods with the more recent and more powerful algorithmic approaches. Trader psychology, cognitive biases and how artificial intelligence is used to increase the efficiency and profitability of trading practices will be illustrated with examples from actual case studies that have been used to teach Algorithmic Trading in the course with the same name that was implemented and has been offered for the past 4 years by the speaker.