There are two function in the basics stats package prcomp() and princomp() and three functions in packages from the French school of data analysis PCA() {FactoMineR} dudi.pca() {ade4} and acp() {amap}.

You will have to look up the documentation for the details, below you will only find some examples for the most common tasks.

princomp (prcomp) performs a principal components analysis on a numeric data matrix and returns the results as an object of class princomp (prcomp).

• princomp(~urb+infmor+lifeem+gnpcap+gnpagr+gnpserv+lit,data=world) Perform a PCA (you can also supply a matrix index of a list of variables (formula style).
• princomp(~urb+infmor+lifeem+gnpcap+gnpagr+gnpserv+lit,data=world, cor=TRUE, scores=TRUE) same, but use correlation matrix (default covariance matrix) and produce factor scores
• pca <- princomp(~urb+infmor+lifeem+gnpcap+gnpagr+gnpserv+lit,data=world, cor=TRUE, scores=TRUE) same, results are stored into pca
• plot(pca) Histogram of the eigenvalues
• summary(pca) display summary of results

• plot(pca$scores) simple plot of the scores stored in the princomp object
• plot(pca$loadings) simple plot of the loadings stored in the princomp object
• bibplot(pca) Produce a biplot (with both scores and loadings (Gabriel's biplot)

A nicer plot for the scores (using {ggplot2}

• scores <-as.data.frame(pca$scores) assign the scores to an object (ggplot requires a data frame)
• ggplot(data = scores, aes(x = Comp.1, y = Comp.2, label = rownames(scores))) + geom_text(colour = "blue", alpha = 0.8, size = 2) + ggtitle("PCA of some world data")

A simple loadings plot with labels (using base graphics); plots by default the first two components

• loadings <-as.matrix(pca$loadings)
• plot(loadings)
• text(loadings,labels=rownames(loadings))

Note this section is very sketchy; there is a lot more in the R Universe

• factanal() {stats} for factor analysis
• Packages FactoMineR and ade4 have many techniques related to correspondence analysis. There is also an explor package for interactive examination and plotting of results from both packages (shiny application).
• cmdscale() {stats} for classical MDS
• isoMDS() {MASS} for Nonmetric MDS
• indscal() {SensoMineR} for individual difference scaling; see also the smacof package).