Would it be considered a Serif or Slab-serif font and why? Thanks:)
First, your example does not show the typical traits of a slab serif: slab serifs usually have equally thick horizontal and vertical strokes, and their serifs are little blocks of the same thickness.
Since your image does show serifs, and your question was whether it is a serif or a slab serif, this is the answer to your question.
Serif: yes. Slab: no.
The logo only shows nine different letters, all of them capitals, and they flow into each other, so the top line does not clearly show the bottom of the letters, the bottom line does not show the top. This makes identification a little difficult (but the experts here, or at the WhatTheFont forums at myfonts.com could probably identify it within seconds).
However, as mentioned in my comment below, your font shows large similarities with the Bell font: not the same, but close, and Robert Bringhurst classifies Bell as an English Neoclassical face, the same category as Baskerville. (Cf. R. Bringhurst. The Elements of Typographic Style. Version 3.1, p. 216)
This would be a Classic Serif, judging by the thick-thin contrast and the fact that the serifs are connected to the rest of the glyph by a 'shoulder', a curved connection.
As Phillipp said in his answer, this is not a slab serif, as those have serifs that are as thick as the glyph's strokes and they usually have little or no thick-thin contrast.