This is a map from the Harvard University Library. There they have high quality scans of all sorts of documents and photos, and the collection focusses on items with no known copyright. Therefore they're free to download and use - like I've done here! This is simply known as G5754_L6E635_1854_H5_1956437818.
Hilliar's Guide for Strangers and Visitors Through Liverpool is an old map originally aimed at the tourist and business traveller. It came as a folded linen map with a card cover.
As with many of these maps, the centre is on Liverpool Town Hall. From here, concentric circles measure outwards every quarter of a mile. A similar measuring tool shows up on the west bank of the Mersey, centres on the Woodside ferry pier.
It's a highly detailed old map of Liverpool, and a lot of the street names are marked on it. As well as the street names, the railway is marked coming in to Exchange Station in the north and Lime Street Station from the south west. Central Station is not marked, as it was built later, in 1874.
The major public buildings are shown, such as the Custom House, the 'Assize Courts' (in St George's Hall) and Kirkdale Gaol.
To the north of Liverpool, where the city has yet to make many inroads into the countryside, you can see field boundaries. The Leeds and Liverpool Canal is marked, as it Kirkdale Industrial School. Mills even appear on the map, with two examples on Bootle Lane.
Hilliard's Map is one of the older maps on this site. As such, it comes from a time when Liverpool was a bustling town, but not yet the bulging metropolis of later decades. If your family is particularly long-lived on Merseyside, then the street names, and the index, will be a great help in family history research.
However, if like me your family came along with the great waves of immigration (Irish, Welsh, Scottish, English and further afield) in the late Victorian period, then you may find their streets were not yet built. In that case, you'd be better off looking at the 1890 Plan of Liverpool, of which the North Sheet and the South Sheet are both available.