Erros na compilação | Angular 2: webapps ainda mais poderosas parte 1

Estou com o seguinte erro. A princípio achei que era outra coisa que não tem nada a ver.
Minha tela mostra apenas a palavra carregando.
Dou o comando npm install, depois npm start na pasta client e ele me retorna as linhas abaixo:
Last login: Thu Feb 23 22:38:08 on ttys001
MacBook-Pro-de-Nuno:~ nunomartins$ cd alurapic
MacBook-Pro-de-Nuno:alurapic nunomartins$ cd client
MacBook-Pro-de-Nuno:client nunomartins$ npm install
npm WARN client@1.0.0 No description
npm WARN client@1.0.0 No repository field.
MacBook-Pro-de-Nuno:client nunomartins$ npm start

> client@1.0.0 start /Users/nunomartins/alurapic/client
> npm run tsc:w


> client@1.0.0 tsc:w /Users/nunomartins/alurapic/client
> tsc -w

app/app.module.ts(3,10): error TS2305: Module '"/Users/nunomartins/alurapic/client/app/app.component"' has no exported member 'AppComponent'.
app/main.ts(6,10): error TS2339: Property 'bootstrapModule' does not exist on type '(extraProviders?: Provider[]) => PlatformRef'.
node_modules/@angular/common/src/directives/ng_class.d.ts(46,34): error TS2304: Cannot find name 'Set'.
node_modules/@angular/compiler/src/compile_metadata.d.ts(347,20): error TS2304: Cannot find name 'Set'.
node_modules/@angular/compiler/src/compile_metadata.d.ts(348,15): error TS2304: Cannot find name 'Set'.
node_modules/@angular/compiler/src/offline_compiler.d.ts(15,26): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/offline_compiler.d.ts(16,38): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/output/output_ast.d.ts(424,63): error TS2304: Cannot find name 'Set'.
node_modules/@angular/compiler/src/template_parser/template_parser.d.ts(45,12): error TS2304: Cannot find name 'Set'.
node_modules/@angular/compiler/src/view_compiler/compile_element.d.ts(33,16): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/view_compiler/compile_query.d.ts(24,49): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/view_compiler/compile_view.d.ts(29,18): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/view_compiler/compile_view.d.ts(52,16): error TS2304: Cannot find name 'Map'.
node_modules/@angular/compiler/src/view_compiler/compile_view.d.ts(54,13): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/change_detection/differs/default_keyvalue_differ.d.ts(24,15): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/change_detection/differs/default_keyvalue_differ.d.ts(28,16): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/di/reflective_provider.d.ts(88,123): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/di/reflective_provider.d.ts(88,165): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(2,25): error TS2304: Cannot find name 'MapConstructor'.
node_modules/@angular/core/src/facade/collection.d.ts(3,25): error TS2304: Cannot find name 'SetConstructor'.
node_modules/@angular/core/src/facade/collection.d.ts(5,27): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(5,39): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(8,9): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(9,30): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(12,43): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(13,27): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(15,23): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(16,25): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/collection.d.ts(101,41): error TS2304: Cannot find name 'Set'.
node_modules/@angular/core/src/facade/collection.d.ts(102,22): error TS2304: Cannot find name 'Set'.
node_modules/@angular/core/src/facade/collection.d.ts(103,25): error TS2304: Cannot find name 'Set'.
node_modules/@angular/core/src/facade/lang.d.ts(12,17): error TS2304: Cannot find name 'Map'.
node_modules/@angular/core/src/facade/lang.d.ts(13,17): error TS2304: Cannot find name 'Set'.
node_modules/@angular/core/src/facade/lang.d.ts(51,59): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/browser/browser_adapter.d.ts(79,33): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/dom/dom_adapter.d.ts(97,42): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/dom/dom_renderer.d.ts(18,37): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(2,25): error TS2304: Cannot find name 'MapConstructor'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(3,25): error TS2304: Cannot find name 'SetConstructor'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(5,27): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(5,39): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(8,9): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(9,30): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(12,43): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(13,27): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(15,23): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(16,25): error TS2304: Cannot find name 'Map'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(101,41): error TS2304: Cannot find name 'Set'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(102,22): error TS2304: Cannot find name 'Set'.
node_modules/@angular/platform-browser/src/facade/collection.d.ts(103,25): error TS2304: Cannot find name 'Set'.
node_modules/rxjs/Observable.d.ts(66,60): error TS2693: 'Promise' only refers to a type, but is being used as a value here.
23:17:08 - Compilation complete. Watching for file changes.
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