This vignette provides a broad introduction to the various facilities in the package. A good place to start if you are new to the package.
If you wish to use model families ala stats::glm, this vignette is for you. The family also includes Cox models for survival, which are discussed in the next vignette below.
Penalized Cox regression models can now be fit in glmnet using both right censored and (start, stop] data. This vignette leads you through the process with several examples.
The idea of the relaxed lasso is to take a glmnet fitted object, and then for each lambda, refit the variables in the active set without any penalization. For details, see below.