The sp-rest-explorer is a wonderful website to explore all the APIs available on SharePoint. You can find it at

For example, if you browse to web > Alert, you can see that the Alert has a method called Add with signature as _api/web/Alerts/Add(...)/. It takes as a parameter, alertCreationInformation which is of type SP.AlertCreationInformation.

And the SP.AlertCreationInformation properties as below.

Property             Type
AlertFrequency       Int32
AlertTemplateName    String
AlertTime            DateTime
AlertType            Int32
AlwaysNotify         Boolean
DeliveryChannels     Int32
EventType            Int32
EventTypeBitmask     Int32
Filter               String
Properties           Collection (SP.KeyValue)
Status               Int32
Title                String

You can post to the endpoint, _api/web/Alerts/Add with the payload

      "Filter":"<Query><And><Or><Eq><FieldRef Name=\"SomeField\"/><Value type=\"string\">Word</Value></Eq><Eq><FieldRef Name=\"SomeField\"/><Value type=\"string\">Excel</Value></Eq></Or><Or><Eq><FieldRef Name=\"SomeSkill\"/><Value type=\"string\">2 - Fortgeschritten</Value></Eq></Or></And></Query>",
      "Title":"My Filtered Notification",

AlertCreationInformation myNewAlert = new AlertCreationInformation();

// myNewAlert.Item = companylibrary.GetItemByUniqueId(alertfolder.UniqueId);
myNewAlert.List = clientContext.Web.Lists.GetByTitle(CompanyType);
myNewAlert.AlertFrequency = AlertFrequency.Immediate;
myNewAlert.AlertTime = DateTime.Now;
myNewAlert.AlertType = AlertType.List;
myNewAlert.AlwaysNotify = true;
myNewAlert.DeliveryChannels = AlertDeliveryChannel.Email;
myNewAlert.EventType = AlertEventType.All;
myNewAlert.Filter = "2";
// 0 = Anything Changes
// 1 = Someone else changes a document
// 2 = Someone else changes a document created by me
// 3 = Someone else changes a document modified by me

myNewAlert.Status = AlertStatus.On;
myNewAlert.Title = "My new alert created at : " + DateTime.Now.ToString();
myNewAlert.User = clientContext.Web.CurrentUser;

var newAlertGuid = clientContext.Web.CurrentUser.Alerts.Add(myNewAlert);