CartoDB uses PostGIS, a powerful add-on for PostgreSQL, to enable spatial database functionality. The blog series focuses on replicating popular GIS software functions using PostGIS queries. Two initial functions covered are Convex Hull and Buffer. A Convex Hull is generated by stretching out a rubber band around a set of points to create the smallest convex polygon that can contain them, useful for highlighting patterns in data or visualizing coverage areas. CartoDB's ST_ConvexHull() function generates a convex hull from a collection of geometries, while SQL statements are used to collect individual points into a geometry collection and transform the result to web mercator coordinates for mapping. A Buffer is created by running a specified distance around another geometry or group of geometries, useful for visual elements on maps or further spatial queries. CartoDB's ST_Buffer() function generates buffers from a geography type column, which can be dissolved into a single feature using ST_Union(). The functions are demonstrated using QGIS and CartoDB datasets, providing examples of how PostGIS can enable efficient data analysis and mapping in GIS software.