Despite its name, Logistic Regression is a classification algorithm, using a linear model (ie, it computes the target feature as a linear combination of input features).

Logistic Regression minimizes a specific cost function (called logit or sigmoid function), which makes it appropriate for classification.
A simple Logistic regression algorithm is prone to overfitting and sensitive to errors in the input dataset. To address these issues, it is possible to use a penalty (or regularization term ) to the weights