The popular linkage methods used in Hierarchical Clustering are as follows:

**Complete-linkage:** In this method, the distance between two clusters is defined as the maximum distance between two data points from each cluster.

**Single-linkage:** In this method, the distance between two clusters is defined as the minimum distance between two data points in each cluster.

**Average-linkage:** In this method, the distance between two clusters is defined as the average distance between each data point in one cluster to every data point in the other cluster.

**Centroid-linkage:** In this method, we find the centroid of cluster 1 and the centroid of cluster 2 and then calculate the distance between the two before merging.