I see in dictionary, that the Dative case of the singular word der Kunde is dem Kunden. Why is there an n in the singular dative case? I would expect dem Kunde, is there some kind of exception here? If so, is there some info about this exception?
This is a special class of masculine nouns. There are actually two subtypes depending on the genitive singular. (Many grammars identify these classes using "strong/mixed/weak" labels, but I've never bothered to learn them myself.) In the most common type, there is an -n ending for every combination except nominative singular. This is the case with Kunde. These nouns are all masculine, and most refer either to human(iod)s, either male or unspecified gender, or to animals, usually large and usually mammals. Another example is Hase which isn't exactly large, but it is a mammal. You can identify these in a dictionary as masculine nouns whose genitive ending is -n instead of -s. In the less common type, there is an -n for every combination except nominative singular and the genitive singular, which ends -ns. Two common examples are Name and Buchstabe. I don't know if there's any kind of pattern for them, but you can identify them in a dictionary as masculine nouns whose genitive ending is -ns. The genitive singular ending for all other nouns is either -s for masculine and neuter, or nothing for feminine, with Herz (neuter) the only exception.
PS. The University of Wisconsin website noted in the comments has good material on grammar, but it is a bit incomplete in places. Another site you might find informative is Grimm Grammar, which has more detail in this case.
These nouns are, according to current terminology, referred to as belonging to the n-Deklination; searching for this term will get you many lists and explanations. Historically, they were referred to as weak nouns (schwache Substantive).
If it weren't for those weak nouns, case inflection of nouns in German would be completely predictable (as opposed to plural inflection, which has to be learned). Rules for case endings of nouns in German, disregarding weak nouns, are as follows:
The only cases that can be marked by a case ending are the genitive singular and the dative plural.1
Feminine nouns do not have any case endings in the singular.
All masculine and neuter nouns have the ending ‑(e)s in the genitive singular.
In the dative plural, all nouns have the case ending ‑(e)n if possible (i.e. if the nominative plural doesn't end in ‑n or ‑s).
When weak nouns enter into the picture, the third rule becomes more complicated.
a. Most masculine nouns (strong and mixed2 nouns) and all neuter nouns3 have ‑(e)s in the genitive singular.
b. A group of masculine nouns (weak nouns) have ‑(e)n or -ens4 in the genitive singular. Those nouns also have ‑(e)n in the accusative and dative singular, contrary to rule 1.
The group of weak nouns has some interesting characteristics.
All masculine nouns ending on unstressed, reduced ‑e (Schwa) belong to this class: Junge, Kunde, Name… (exception: Käse)
Many nouns belonging to this class refer to animate beings: Athlet, Held, Herr, Nachbar, Mensch, Pilot, Soldat…
Many words with endings of foreign origin belong to this class: Automat, Fotograf, Planet, Präsident…
All weak nouns form the plural with ‑(e)n.
As you can see, your intuition that these nouns are special is justified.
1 Let's disregard moribund dative singular ‑e.
2 "Mixed" nouns is a historical term for those nouns that have ‑(e)s in the singular, but ‑(e)n in the plural.
3 There is exactly one neuter noun that can inflect weakly: das Herz, im Herzen, des Herzens.
4 The small group of nouns with ‑ns in the genitive singular such as Gedanke, Name, Wille are not considered to be weak nouns in some grammars, but it is practical to subsume them under that label.