Hello everyone, I am learning normalizations, I wonder when log2 and quantile normalization is used in each situation, may I ask if there is any material that compare these two types especially in microarray expression matrix for differentially expressed gene analysis? Thank you!

Taking logs and doing a quantile normalization are completely different things, so there is no sense in comparing them. In addition, this support site is intended for helping people who are having problems understanding Bioconductor tools, rather than general questions about data transformations. A better choice for those sorts of questions would be biostars or stackoverflow.