The Pandas library in Python provides various tools for reading, manipulating, and presenting data. The pivot() function is used to transform a DataFrame into a new one by converting selected columns into new columns based on their values. This operation allows for better understanding of the data and efficient comparison of different datasets. The pivot_table() function is more powerful than pivot(), enabling the creation of summary tables of data by pivoting on one or more columns and aggregating values across one or more columns. It provides flexibility and functionality compared to pivot(). The melt() function is used to transform data from wide format to long format, useful when working with datasets that have been pivoted or transposed. Understanding the differences between these functions and knowing when to use them can greatly benefit data analysis and visualization in Python.