The two main methods for analyzing securities (stocks, options, etc.) are technical analysis and fundamental analysis. Quantitative analysis is newer and combines aspects of both via software.
Technical analysis believes that all relevant info is reflected by price. It uses past data (price, volume, time) dynamics to predict future price movements. It can be visual as it involves identifying commmon chart patterns that are empirically known to predict outcomes. It is universally applicable to all securities and to both short-term and long-term trading. Its reliability increases volume (sample size) is higher.
Fundamental analysis believes that securities are either overvalued or undervalued, and that this price difference will be realized over time. It researches companies' financial earnings, competitors, economics, and news in order to predict price direction. It is more applicable to long-term than short-term trading.
Quantitative analysis deploys mathematics and software in order to programmatically predict price changes. It aims to optimize trades via iterative or statistical algorithms based on both technical and fundamental data. Its algorithmic nature makes it more applicable at scale. Quantitative models are complex and their implementation requires software.