When I come across a notion from algebra or number theory which I don't know I usually check Keith Conrad's page to see if he has written something about it. Key features of his articles are a very clear exposition and carefully worked-out, well-chosen examples. Furthermore, he explains why the definitions are the way the are (why do we require a subring of a unital ring to have the same multiplicative identy as the original ring?).
I am now looking for articles of similar style and quality explaining the basic notions of analysis (both real and complex analysis) and probability theory (so they should be aimed at undergraduate students). More specifically, I mean the notions (and central theorems) you would expect to learn in any undergraduate course on the subject at a German university. The content descriptions of the courses in the following document might give you an idea of what that means: mathematics.uni-bonn.de/study/master/files/MA_QualTest.pdf The courses are: Analysis I & II (page 2), Analysis III (page 3), Introduction to complex analysis (p. 4), Introduction to Probability & Stochastik Processes (both p. 6).
I tried to find something using google and the only thing I found is http://www.mtts.org.in/expository-articles. There are articles on theorems from analysis on that site, but they focus on proofs and do not contain enough motivation for definitions or interesting examples (as far as I checked, I did not read them all). The articles should not be too dense (to give you an idea of what that means: They should not be as dense and short as the articles in the Princeton Companion).
Note that I am looking for articles which are available freely online.
I am aware of the related question Elementary Papers at ArXiv, however, I ask for articles explaining ideas and notions from analysis and probability theory only and do not require the articles to be posted on the arxiv.