In Adobe Photoshop I am able to select multiple layers at once with Shift+Click.
How can I do that in GIMP?
It's not possible. The only thing you can do is link layers together or merge them. How to link layers information here.
Instead, there are several alternative methods of handling multiple layers, each appropriate to a different task. You can chain layers to move or transform them, shift-click objects on different layers in the canvas to align them, or create a new layer based on all visible layers.
1) Make sure the Layers dialog box is open. If it is not, click on the Windows menu and select "Dockable Dialogs" > "Layers." You can also hold down the "Ctrl" key and press "L."
2) Hover your mouse between the Layer Visibility icon, which looks like an eye, and the layer thumbnail. A raised box will appear. Click this box to activate the chain.
3) Repeat this process on all of the other layers you wish to chain together. Once these layers are chained, you can move or apply transformation effects to all of them simultaneously.
Selecting for Alignment
4) Make sure the Toolbox is open. If it is not, click on the Windows menu and select "Toolbox." You can also hold down the "Ctrl" key and press "B."
5) Click on the Alignment Tool in the Toolbox. It looks like an empty rectangle with arrows pointing away from all sides of it.
6) Press and hold the "Shift" key while clicking on the layers in the canvas. Or click somewhere off the layers and drag a selection rectangle around them. Once you have selected these layers, you can choose an alignment method.
Merging Visible Layers
7) Make sure the Layers dialog box is open. If it is not, click on the Windows menu and select "Dockable Dialogs" > "Layers." You can also hold down the "Ctrl" key and press "L."
8) Click on the Visibility icon on any layer you do not want to include in your new layer. This will render that layer invisible.
9) Click on the Layers menu and select "New from Visible."
10) Select the option that best describes how you want the layers to be merged from the dialog box that appears, and click "Merge." This will merge all of the visible layers into a new layer but will not affect your original layers.
You can (from 2.8 on) make use of layer groups to get most of the functionality you might want:
From the GIMP docs:
You can create a layer group either by
Clicking on the Create a new layer group button at the bottom of the layer dialog (looks like a folder icon)
Through Layer → New Layer Group, or
Through the layer dialog context menu.
You can drag existing layers into the new Layer Group to add them. Then, transformations (move, scale etc.) applied to the Group as a whole will be performed on all the layers in that group.
In GIMP 2.10, this is now possible. Thanks to @Michael Schumacher for the bug link: https://bugzilla.gnome.org/show_bug.cgi?id=730216
This is not possible in GIMP, up to and including 2.8.x.
If and when it is available (in the then-current development branch at least), then the corresponding enhancement request at https://bugzilla.gnome.org/show_bug.cgi?id=730216 will be marked resolved fixed.
It is becoming available in the current development branch - that is, GIMP 2.99.x - see https://gitlab.gnome.org/GNOME/gimp/-/issues/557 (the same issue as the one linked before, in a new issue tracker).
User interaction is not complete yet, but at least it's a start.
Here is the Essential Visual-Tip: http://tutorialforlinux.com/2014/08/01/how-to-select-more-layers-on-the-gimp-for-linux-mac-windows-easy-visual-guide/