What is the difference between にかんして and について? Example usage would be much appreciated!
に関して => Related to, in relation to について => Concerning, along, under, per
この問題に関して質問を受ける Be questioned in relation with this problem
この点に関しての米国の見方は、各国が必要とする行動には差異があるということです。 The view of the United States on this point is that there is differentiation in what countries need to do
（人）の学校での一日について話し合う Discuss someone's day at school
2年目はロボット工学や宇宙科学の発達について学びます。 In the second year, the students will learn about robot technology and the development of space science.
In many contexts, they can both be translated to English as variations of "related", "as for" etc, but there are some differences...
As far as I know (and could find from different Japanese grammar sources), a few of the nuances are:
Edit: a large part of the above examples are taken from the very link mentioned by phirru below: it is indeed a nice page on the topic. However, I found the explanations a lot more confusing than in my other grammar books (and decided not to go for a full translation).
I found the answer on this website to be incredibly useful and explained the difference in a very understandable way: http://nihon5ch.net/contents/bbs-study/old/mie-bbs.cgi?s=86
However, I've quickly attempted to do a rough translation of the important parts of the answer so that even beginners who see this question can understand the difference. If able, I highly recommend reading the original post, however.
Usage Context/Literary Differences
When studying Japanese, 「〜について／〜についての」is studied before 「〜に関する／関して」. That is to say, 「〜について」is often used as a basic phrase in conversation.
In the case of foreign language study, when you translate into your own language and the words come out the same the difference can be difficult to understand. However, there is the following difference. 「〜について」→ Expression used often in conversation. 「〜に関して」→ Expression often used in written language.
About The Differences In Usage
1) The meaning of「○○について～する」
With verbs like 「話す」and 「考える」, for the reason of stating the topic or theme about which you intend to speak or think about first, 「について話す／考える」is used. In other words, if you were to say 「自分の夢について話す」, it would be because you are going to talk about things like 1) What you want to be, 2) Why you want to be that, 3) How you're going to become what you want to be.
2) The meaning of 「○○に関して〜する」
The meaning of 「関する」is "to be related", "to have a connection". Therefore, the expression 「○○に関して〜する」is used with the meaning of "In relation/connection to ○○ I/He/It will 〜". That is to say, much like 「について」it displays the theme or topic, however it is not restricted to just THAT topic. Of course 「○○に関して〜する」indicates a direct relation to ○○, however, it indicates strongly that related and connected topics will also be addressed.
If you picture the above description as an image, I think the difference can be understood easily.
If you were to say「日本語について研究する」, it would have the theme of 「日本語」and be restricted to content such as 「日本語の単語」、「日本語の文法」and 「日本語の発音」.
However, If you were to say 「日本語に関して研究する」, 「日本語」would be centered on, however it would point out that it is not "restricted" and areas peripheral to the topic are included.
For example, things like:
So, if you were going to be writing about Japanese festivals (What is interesting, what type of festivals you like, etc), you normally say "日本のお祭りについて書く". If however, you were to say 「日本のお祭りに関して書く」, it gives the impression that you will be centering around festivals but also touching on related topics. Additionally, it gives a much "stiffer" impression than "について".
（Ａ）「～について ＋ Predicate」（Predicate：Verb、Noun ＋ Verb)
（Ｂ）「～についての ＋ Noun」
（Ｃ）「～に関して ＋ Predicate」
（Ｄ）「～に関する ＋ Noun」
I think it's just important to look at the kanjis to get the meaning.
「に関する」means "to have a link with, to be related to".
Those two meanings are different: one is concrete (ついて) one is meta (関して). Either you literally discuss the contents (ついて) either you discuss what revolves around (関して).