In a Romantic song cycle or songbook, songs tend to share many common ideas because they are used to set to the poems from one collection written or collected by one author. Many composers designed the same motivic or structural elements to a group of songs for unity, and sometimes they made chronological narratives for the series of poems. Music theorists have tried to find out a way of giving a sense of unity or narrative to the songs in a song cycle or songbook by analyzing its musical language and text setting. They have suggested plausible explanations for the relationships among the songs in a song cycle or songbook, and some theorists have traced the tonal movements and provided a visual explanation for them. Hugo Wolf's two volumes of the Italienisches Liederbuch (1890-91, 1896) were set to the forty-six poems from Paul Heyse's well-selected works. Wolf's way of selecting poems from Heyse's collection seems inconsistent, and his song ordering in the both volumes does not show evident rules. However, a closer study for relationships between the songs could widen our perspective to comprehend the whole songbook as a unified storyline. This study selected the first four songs from each volume of the Italienisches Liederbuch, and analyzed the eight songs in a traditional way, accounting for harmony, motivic feature, tonal movement, form, and text setting. The study finds that Wolf used the third relationships among the songs to convey a storyline in his order of the songs, and especially exploited the direction of thirds for his own narrative. While this may only be a pilot study with partial results, it can serve as a stimulus for a comprehensive study of factors that provide unity in the cycle as a whole.