in principle, as Kevin said, GEOquery should download the processed expression profiles using the function getGEO(). however, i'm afraid in the case of GSE117134 this is not going to work because those expression profiles seem to be stored as supplementary file in GEO. to access them you can do the following:

download.file("https://www.ncbi.nlm.nih.gov/geo/download/?acc=GSE117134&format=file&file=GSE117134%5Fcasava%5Fgene%5Fexpression%2Etsv%2Egz", "GSE117134_casava_gene_expression.tsv.gz")
y <- read.csv("GSE117134_casava_gene_expression.tsv.gz", sep="\t")
dim(y)
[1] 18079    55
y[1:5, 1:5]
    Gene WT_ZT00_BR1 WT_ZT00_BR2 WT_ZT00_BR3 WT_ZT04_BR1
1   Xkr4     0.01436     0.00000     0.00955     0.00834
2  Sox17     0.61960     0.42963     0.38794     0.41122
3 Mrpl15    15.12894    17.25888    14.15717    12.10911
4 Lypla1    53.79726    76.55921    69.43295    58.77200
5  Tcea1     5.47423     5.52237     5.04543     5.20710

because read.csv() outputs a data.frame object you might want to transform it into a matrix as follows:

genesymbols <- y$Gene
y <- as.matrix(y[, -1])
rownames(y) <- genesymbols
y[1:5, 1:5]
       WT_ZT00_BR1 WT_ZT00_BR2 WT_ZT00_BR3 WT_ZT04_BR1 WT_ZT04_BR2
Xkr4       0.01436     0.00000     0.00955     0.00834     0.00000
Sox17      0.61960     0.42963     0.38794     0.41122     0.47293
Mrpl15    15.12894    17.25888    14.15717    12.10911    16.77634
Lypla1    53.79726    76.55921    69.43295    58.77200    82.90862
Tcea1      5.47423     5.52237     5.04543     5.20710     5.84447

and now you're ready to analyze the gene expression data matrix in y. A starting point for a beginner may be any of the available workflows for this kind of data, such as this one or this other one, taking into account that your starting point are not RNA-seq raw counts but RNA-seq processed expression profiles in some kind of continuous units of expression, check the associated publication to learn what kind of units are those and how they have been processed.